Question 1

Add or subtract. Assume all variables represent nonnegative real numbers.
- 6x12y11−5xxy116 \sqrt [ 11 ] { \mathrm { x } ^ { 12 } \mathrm { y } } - 5 \mathrm { x } \sqrt [ 11 ] { \mathrm { xy } }611x12y​−5x11xy​

Accepted Answer

A)    xxy11x \sqrt [ 11 ] { x y }x11xyc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    2xxy112 x \sqrt [ 11 ] { x y }2x11xyc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    6xy11−2xxy116 \sqrt [ 11 ] { x y } - 2 x \sqrt [ 11 ] { x y }611xyc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​−2x11xyc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)   Cannot simplify E) None of the above
F) All of the above

Question 2

Multiply.
--4i ∙ 5i

Accepted Answer

A)   9
B)   20
C)   -9
D)  -20D) None of the above
E) All of the above

Question 3

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
- 405x2\sqrt { 405 x ^ { 2 } }405x2​

Accepted Answer

A)    405x405 x405x 
B)    95x9 \sqrt { 5 x }95xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    9x9 x9x 
D)    9x59 x \sqrt { 5 }9x5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​E) A) and B)
F) A) and C)

Question 4

Rationalize the denominator and simplify.
- 57−5\frac { 5 } { 7 - \sqrt { 5 } }7−5​5​

Accepted Answer

A)    35+55−2\frac { 35 + 5 \sqrt { 5 } } { - 2 }−235+55c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)    35+5544\frac { 35 + 5 \sqrt { 5 } } { 44 }4435+55c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    35−5544\frac { 35 - 5 \sqrt { 5 } } { 44 }4435−55c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
D)    57−55\frac { 5 } { 7 } - \frac { 5 } { \sqrt { 5 } }75​−5c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​5​E) C) and D)
F) A) and D)

Question 5

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
- −3433\sqrt [ 3 ] { - 343 }3−343​

Accepted Answer

A)   7
B)   19
C)   49
D)   -7 E) B) and C)
F) A) and D)

Question 6

Simplify by rationalizing the denominator. Write your answer in a +bi form.
- 2+2i7−6i\frac { 2 + 2 i } { 7 - 6 i }7−6i2+2i​

Accepted Answer

A)    2−2i2 - 2 \mathrm { i }2−2i 
B)    2685+285i\frac { 26 } { 85 } + \frac { 2 } { 85 } \mathrm { i }8526​+852​i 
C)    285+2685i\frac { 2 } { 85 } + \frac { 26 } { 85 } \mathrm { i }852​+8526​i 
D)    213−2i\frac { 2 } { 13 } - 2 i132​−2iE) None of the above
F) B) and D)

Question 7

Solve the problem. Round the answer to the nearest hundredth.
-A pendulum has a length of 2.4 feet. Find its period. Use the formula  T=2πL32\mathrm { T } = 2 \pi \sqrt { \frac { \mathrm { L } } { 32 } }T=2π32L​​

Accepted Answer

A)   0.86 sec
B)   2.15 sec
C)   1.72 sec
D)   1.22 sec E) A) and B)
F) A) and C)

Question 8

Rationalize the denominator and simplify.
- 23+137107−33\frac { 2 \sqrt { 3 } + 13 \sqrt { 7 } } { 10 \sqrt { 7 } - 3 \sqrt { 3 } }107​−33​23​+137​​

Accepted Answer

A)    5921+928727\frac { 59 \sqrt { 21 } + 928 } { 727 }7275921c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​+928​ 
B)    5921+63+1307673\frac { 59 \sqrt { 21 } + 6 \sqrt { 3 } + 130 \sqrt { 7 } } { 673 }6735921c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​+63c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​+1307c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    2167727\frac { 2167 } { 727 }7272167​ 
D)    5921+928673\frac { 59 \sqrt { 21 } + 928 } { 673 }6735921c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​+928​E) B) and D)
F) C) and D)

Question 9

Add or subtract. Assume all variables represent nonnegative real numbers.
- 10x74−4xx3410 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }104x7​−4x4x3​

Accepted Answer

A)    6xx746 x \sqrt [ 4 ] { x ^ { 7 } }6x4x7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    10x74−4xx3410 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }104x7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​−4x4x3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    6xx346 x \sqrt [ 4 ] { x ^ { 3 } }6x4x3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    14x3414 \sqrt [ 4 ] { x ^ { 3 } }144x3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​E) All of the above
F) A) and C)

Question 10

Multiply.
- (7+7) 2( 7 + \sqrt { 7 } )  ^ { 2 }(7+7​) 2

Accepted Answer

A)    49+14749 + 14 \sqrt { 7 }49+147c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    14+14714 + 14 \sqrt { 7 }14+147c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    56+7756 + 7 \sqrt { 7 }56+77c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    56+14756 + 14 \sqrt { 7 }56+147c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​E) None of the above
F) C) and D)

Question 11

Multiply. Write your answer in a + bi form.
- (8+3i) (3+3i) ( 8 + 3 i )  ( 3 + 3 i ) (8+3i) (3+3i)

Accepted Answer

A)    33−15i33 - 15 \mathrm { i }33−15i 
B)    15−33i15 - 33 \mathrm { i }15−33i 
C)    15+33i15 + 33 \mathrm { i }15+33i 
D)    9i2+33i+249 i ^ { 2 } + 33 i + 249i2+33i+24E) B) and D)
F) C) and D)

Question 12

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
- xy53⋅x19y143\sqrt [ 3 ] { x y ^ { 5 } } \cdot \sqrt [ 3 ] { x ^ { 19 } y ^ { 14 } }3xy5​⋅3x19y14​

Accepted Answer

A)    x6y6xy23x ^ { 6 } y ^ { 6 } \sqrt [ 3 ] { x y ^ { 2 } }x6y63xy2c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067l0 -0c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60zM1001 80h400000v40h-400000z'/>​ 
B)    x6y7xy3x ^ { 6 } y ^ { 7 } \sqrt [ 3 ] { x y }x6y73xyc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    x6y7x2y23x ^ { 6 } y ^ { 7 } \sqrt [ 3 ] { x ^ { 2 } y ^ { 2 } }x6y73x2y2c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067l0 -0c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60zM1001 80h400000v40h-400000z'/>​ 
D)    x6y6x2y3x ^ { 6 } y ^ { 6 } \sqrt [ 3 ] { x ^ { 2 } y }x6y63x2yc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067l0 -0c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60zM1001 80h400000v40h-400000z'/>​E) All of the above
F) A) and B)

Question 13

Solve. Check for extraneous solutions.
- (x−6) 1/2=−2( x - 6 )  ^ { 1 / 2 } = - 2(x−6) 1/2=−2

Accepted Answer

A)    {4}\{ 4 \}{4} 
B)    {10}\{ 10 \}{10} 
C)    {16}\{ 16 \}{16} 
D)    ∅ \varnothing ∅E) A) and B)
F) None of the above

Question 14

Solve the problem.
-The radius of a sphere depends on its surface area, S, and is given by the formula  r=S4πr = \sqrt { \frac { S } { 4 \pi } }r=4πS​​

Accepted Answer

A)   98.5 square inches
B)   17.6 square inches
C)   393.9 square inches
D)   70.3 square inches E) None of the above
F) A) and B)

Question 15

Write the word or phrase that best completes each statement or answers the question.
-Choose values for n, a, and b to demonstrate the truth or falsity of the statement: $\sqrt [ n ] { a } + \sqrt [ n ] { b } = \sqrt [ n ] { a + b }$

Accepted Answer

The statem...

Question 16

Find the missing complex number.
-(4 - 2i)  + ? = 7 + 3i

Accepted Answer

A)   -7 - 3i
B)   3 + 5i
C)   1 + 7i
D)   7 - 3iE) B) and D)
F) All of the above

Question 17

Solve the problem.
-For the function  f(x) =6x+63+4f ( x )  = \sqrt [ 3 ] { 6 x + 6 } + 4f(x) =36x+6​+4 , find all values  xxx  for which  f(x) =8f ( x )  = 8f(x) =8

Accepted Answer

A)    9239 \frac { 2 } { 3 }932​ 
B)    543\sqrt [ 3 ] { 54 }354c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    1231 \frac { 2 } { 3 }132​ 
D)    832383 \frac { 2 } { 3 }8332​E) C) and D)
F) B) and D)

Question 18

Simplify.
-i 10

Accepted Answer

A)    −1- 1−1 
B)    i\mathrm { i }i 
C)    −i- \mathrm { i }−i 
D)   1 E) B) and C)
F) A) and B)

Question 19

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
- x6y10z36\sqrt [ 6 ] { x ^ { 6 } y ^ { 10 } z ^ { 3 } }6x6y10z3​

Accepted Answer

A)    xyy4z3x y \sqrt { y ^ { 4 } z ^ { 3 } }xyy4z3c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067l0 -0c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60zM1001 80h400000v40h-400000z'/>​ 
B)    xyzy4z36x y z \sqrt [ 6 ] { y ^ { 4 } z ^ { 3 } }xyz6y4z3c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067l0 -0c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60zM1001 80h400000v40h-400000z'/>​ 
C)    xyy4z36x y \sqrt [ 6 ] { y ^ { 4 } z ^ { 3 } }xy6y4z3c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067l0 -0c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60zM1001 80h400000v40h-400000z'/>​ 
D)    xy4z36x \sqrt [ 6 ] { \mathrm { y } ^ { 4 } \mathrm { z } ^ { 3 } }x6y4z3c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067l0 -0c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60zM1001 80h400000v40h-400000z'/>​E) A) and D)
F) A) and C)

Question 20

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers.
- 45x3y5\sqrt { \frac { 45 x ^ { 3 } } { y 5 } }y545x3​​

Accepted Answer

A)    3xy25xy\frac { 3 x } { y 2 } \sqrt { \frac { 5 x } { y } }y23x​y5x​l0 -0c4,-6.7,10,-10,18,-10 H400000v40H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744c-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5c53.7,-170.3,84.5,-266.8,92.5,-289.5zM1001 80h400000v40h-400000z'/>​ 
B)    x45xyy3\frac { x \sqrt { 45 x y } } { y 3 }y3x45xyc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
C)    3x5xyy3\frac { 3 x \sqrt { 5 x y } } { y 3 }y33x5xyc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
D)    3x35y5\frac { 3 x ^ { 3 } \sqrt { 5 } } { y 5 }y53x35c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​E) A) and B)
F) All of the above

Exam 9: Radical Expressions and Equations

Solve the problem. -The radius of a sphere depends on its surface area, S, and is given by the formula r=S4πr = \sqrt { \frac { S } { 4 \pi } }r=4πS​​

Correct AnswerverifiedShow Answer

Solve. Check for extraneous solutions. - (x−6) 1/2=−2( x - 6 ) ^ { 1 / 2 } = - 2(x−6) 1/2=−2

Correct AnswerverifiedShow Answer

Multiply. Write your answer in a + bi form. - (8+3i) (3+3i) ( 8 + 3 i ) ( 3 + 3 i ) (8+3i) (3+3i)

Correct AnswerverifiedShow Answer

Rationalize the denominator and simplify. - 23+137107−33\frac { 2 \sqrt { 3 } + 13 \sqrt { 7 } } { 10 \sqrt { 7 } - 3 \sqrt { 3 } }107​−33​23​+137​​

Correct AnswerverifiedShow Answer

Add or subtract. Assume all variables represent nonnegative real numbers. - 6x12y11−5xxy116 \sqrt [ 11 ] { \mathrm { x } ^ { 12 } \mathrm { y } } - 5 \mathrm { x } \sqrt [ 11 ] { \mathrm { xy } }611x12y​−5x11xy​

Correct AnswerverifiedShow Answer

Multiply. - (7+7) 2( 7 + \sqrt { 7 } ) ^ { 2 }(7+7​) 2

Correct AnswerverifiedShow Answer

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - −3433\sqrt [ 3 ] { - 343 }3−343​

Correct AnswerverifiedShow Answer

Simplify by rationalizing the denominator. Write your answer in a +bi form. - 2+2i7−6i\frac { 2 + 2 i } { 7 - 6 i }7−6i2+2i​

Correct AnswerverifiedShow Answer

Multiply. --4i ∙ 5i

Correct AnswerverifiedShow Answer

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - 405x2\sqrt { 405 x ^ { 2 } }405x2​

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Write the word or phrase that best completes each statement or answers the question. -Choose values for n, a, and b to demonstrate the truth or falsity of the statement: an+bn=a+bn\sqrt [ n ] { a } + \sqrt [ n ] { b } = \sqrt [ n ] { a + b }na​+nb​=na+b​

Correct AnswerverifiedThe statem...View AnswerShow Answer

Find the missing complex number. -(4 - 2i) + ? = 7 + 3i

Correct AnswerverifiedShow Answer

Add or subtract. Assume all variables represent nonnegative real numbers. - 10x74−4xx3410 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }104x7​−4x4x3​

Correct AnswerverifiedShow Answer

Simplify. -i 10

Correct AnswerAnswered by ExamLex AIShow Answer

Solve the problem. -For the function f(x) =6x+63+4f ( x ) = \sqrt [ 3 ] { 6 x + 6 } + 4f(x) =36x+6​+4 , find all values xxx for which f(x) =8f ( x ) = 8f(x) =8

Correct AnswerverifiedShow Answer

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - x6y10z36\sqrt [ 6 ] { x ^ { 6 } y ^ { 10 } z ^ { 3 } }6x6y10z3​

Correct AnswerverifiedShow Answer

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - xy53⋅x19y143\sqrt [ 3 ] { x y ^ { 5 } } \cdot \sqrt [ 3 ] { x ^ { 19 } y ^ { 14 } }3xy5​⋅3x19y14​

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Solve the problem. Round the answer to the nearest hundredth. -A pendulum has a length of 2.4 feet. Find its period. Use the formula T=2πL32\mathrm { T } = 2 \pi \sqrt { \frac { \mathrm { L } } { 32 } }T=2π32L​​

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Rationalize the denominator and simplify. - 57−5\frac { 5 } { 7 - \sqrt { 5 } }7−5​5​

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Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers. - 45x3y5\sqrt { \frac { 45 x ^ { 3 } } { y 5 } }y545x3​​

Correct AnswerverifiedShow Answer

Solve the problem. -The radius of a sphere depends on its surface area, S, and is given by the formula $r = \sqrt { \frac { S } { 4 \pi } }$

Correct Answer
verified

Solve. Check for extraneous solutions. - $( x - 6 ) ^ { 1 / 2 } = - 2$

Correct Answer
verified

Multiply. Write your answer in a + bi form. - $( 8 + 3 i ) ( 3 + 3 i )$

Correct Answer
verified

Rationalize the denominator and simplify. - $\frac { 2 \sqrt { 3 } + 13 \sqrt { 7 } } { 10 \sqrt { 7 } - 3 \sqrt { 3 } }$

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Add or subtract. Assume all variables represent nonnegative real numbers. - $6 \sqrt [ 11 ] { \mathrm { x } ^ { 12 } \mathrm { y } } - 5 \mathrm { x } \sqrt [ 11 ] { \mathrm { xy } }$

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Multiply. - $( 7 + \sqrt { 7 } ) ^ { 2 }$

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Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt [ 3 ] { - 343 }$

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Simplify by rationalizing the denominator. Write your answer in a +bi form. - $\frac { 2 + 2 i } { 7 - 6 i }$

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Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt { 405 x ^ { 2 } }$

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Write the word or phrase that best completes each statement or answers the question. -Choose values for n, a, and b to demonstrate the truth or falsity of the statement: $\sqrt [ n ] { a } + \sqrt [ n ] { b } = \sqrt [ n ] { a + b }$

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The statem...
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Add or subtract. Assume all variables represent nonnegative real numbers. - $10 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$

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Simplify. -i¹⁰

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Solve the problem. -For the function $f ( x ) = \sqrt [ 3 ] { 6 x + 6 } + 4$ , find all values $x$ for which $f ( x ) = 8$

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Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt [ 6 ] { x ^ { 6 } y ^ { 10 } z ^ { 3 } }$

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Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $\sqrt [ 3 ] { x y ^ { 5 } } \cdot \sqrt [ 3 ] { x ^ { 19 } y ^ { 14 } }$

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Solve the problem. Round the answer to the nearest hundredth. -A pendulum has a length of 2.4 feet. Find its period. Use the formula $\mathrm { T } = 2 \pi \sqrt { \frac { \mathrm { L } } { 32 } }$

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Rationalize the denominator and simplify. - $\frac { 5 } { 7 - \sqrt { 5 } }$

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Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers. - $\sqrt { \frac { 45 x ^ { 3 } } { y 5 } }$

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