Question 1

Find the square root. Assume that all variables represent nonnegative real numbers.
-$\sqrt { 256 }$

Accepted Answer

A)  128 
B)  16 
C)  17 
D)  not a real number 
A)  128 
B)  16 
C)  17 
D)  not a real number

Question 2

Find the midpoint of the line segment whose endpoints are given.
-$( 4,7 ) , ( 8,5 )$

Accepted Answer

A)  $( - 4,2 )$ 
B)  $( 12,12 )$ 
C)  $( 6,6 )$ 
D)  $( - 2,1 )$ 
A)  $( - 4,2 )$ 
B)  $( 12,12 )$ 
C)  $( 6,6 )$ 
D)  $( - 2,1 )$

Question 3

Solve.
-$$\sqrt { x + 2 } = 2$$

Accepted Answer

A)  6 
B)  2 
C)  4 
D)  16 
A)  6 
B)  2 
C)  4 
D)  16

Question 4

Find the midpoint of the line segment whose endpoints are given.
-$( - 9 , - 9 ) , ( 2,1 )$

Accepted Answer

A)  $( - 11 , - 10 )$ 
B)  $( - 7 , - 8 )$ 
C)  $\left( - \frac { 7 } { 2 } , - 4 \right)$ 
D)  $\left( - \frac { 11 } { 2 } , - 5 \right)$ 
A)  $( - 11 , - 10 )$ 
B)  $( - 7 , - 8 )$ 
C)  $\left( - \frac { 7 } { 2 } , - 4 \right)$ 
D)  $\left( - \frac { 11 } { 2 } , - 5 \right)$

Question 5

Use rational exponents to write as a single radical expression.
-$\frac { \sqrt [ 8 ] { \mathrm { y } } } { \sqrt [ 9 ] { \mathrm { y } } }$

Accepted Answer

A)  $y$ 
B)  $\frac { 1 } { \Gamma }$ 
C)  $\sqrt [ 9 ] { \mathrm { y } ^ { 8 } }$ 
D)  $\sqrt [ 72 ] { y }$ y 
A)  $y$ 
B)  $\frac { 1 } { \Gamma }$ 
C)  $\sqrt [ 9 ] { \mathrm { y } ^ { 8 } }$ 
D)  $\sqrt [ 72 ] { y }$ y

Question 6

Use radical notation to write the expression. Simplify if possible.
-$$- \left( \frac { 81 } { 256 } \right) ^ { 1 / 4 }$$

Accepted Answer

A)  $\frac { 3 } { 5 }$ 
B)  $\frac { 3 } { 4 }$ 
C)  $- \frac { 1 } { 2 }$ 
D)  $- \frac { 3 } { 4 }$ 
A)  $\frac { 3 } { 5 }$ 
B)  $\frac { 3 } { 4 }$ 
C)  $- \frac { 1 } { 2 }$ 
D)  $- \frac { 3 } { 4 }$

Question 7

Solve.
-Find the area of the trapezoid. Simplify if possible.

Accepted Answer

A)  $741 \sqrt { 55 }$ sq. $\mathrm { m }$ 
B)  $114 \sqrt { 11 }$ sq. $\mathrm { m }$ 
C)  $228 \sqrt { 55 }$ sq. m 
D)  $114 \sqrt { 55 } \mathrm { sq } . \mathrm { m }$ 
A)  $741 \sqrt { 55 }$ sq. $\mathrm { m }$ 
B)  $114 \sqrt { 11 }$ sq. $\mathrm { m }$ 
C)  $228 \sqrt { 55 }$ sq. m 
D)  $114 \sqrt { 55 } \mathrm { sq } . \mathrm { m }$

Question 8

Write with positive exponents. Simplify if possible.
-$\frac { 7 } { 6 x ^ { - 2 / 7 } }$

Accepted Answer

A)  $42 x ^ { 2 / 7 }$ 
B)  $\frac { 6 x ^ { 2 / 7 } } { 7 }$ 
C)  $\frac { 7 x ^ { 2 / 7 } } { 6 }$ 
D)  $\frac { 36 ^ { 1 / 7 } x ^ { 2 / 7 } } { 7 }$ 
A)  $42 x ^ { 2 / 7 }$ 
B)  $\frac { 6 x ^ { 2 / 7 } } { 7 }$ 
C)  $\frac { 7 x ^ { 2 / 7 } } { 6 }$ 
D)  $\frac { 36 ^ { 1 / 7 } x ^ { 2 / 7 } } { 7 }$

Question 9

Solve.
-Find the perimeter of the trapezoid. Simplify.

Accepted Answer

A)  $34 \sqrt { 3 }$ in. 
B)  $35 \sqrt { 3 }$ in. 
C)  $( 20 \sqrt { 3 } + 3 \sqrt { 75 } )$ in. 
D)  17,325 in. 
A)  $34 \sqrt { 3 }$ in. 
B)  $35 \sqrt { 3 }$ in. 
C)  $( 20 \sqrt { 3 } + 3 \sqrt { 75 } )$ in. 
D)  17,325 in.

Question 10

Use the product rule to multiply. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { 216 } \cdot \sqrt [ 3 ] { 729 }$$

Accepted Answer

A)  15 
B)  $- 3$ 
C)  $- 54$ 
D)  54 
A)  15 
B)  $- 3$ 
C)  $- 54$ 
D)  54

Question 11

Solve.
-$$\sqrt { \mathrm { x } } - 2 = \sqrt { \mathrm { x } + 32 }$$

Accepted Answer

A)  $x = - 49$ 
B)  $x = - 7$ 
C)  $x = 49$ 
D)  $\varnothing$ 
A)  $x = - 49$ 
B)  $x = - 7$ 
C)  $x = 49$ 
D)  $\varnothing$

Question 12

Find all real square roots of the number.
1849

Accepted Answer

A)   45, -45 
B)   43, -43 
C)   86, -86 
D)   44, -44 
A)   45, -45 
B)   43, -43 
C)   86, -86 
D)   44, -44

Question 13

Fill in the blank with one of the words or phrases listed below.

-The ـــــــــــــــــof a nonnegative number a is written as $\sqrt { a }$.

Accepted Answer

A)  principal square root 
B)  conjugate 
C)  index 
D)  radicand 
A)  principal square root 
B)  conjugate 
C)  index 
D)  radicand

Question 14

Simplify. Assume that all variables represent positive real numbers.
-$\frac { \sqrt [ 3 ] { 12 } } { \sqrt [ 3 ] { 6 } }$

Accepted Answer

A)  $\sqrt [ 3 ] { 6 }$ 
B)  $\frac { 1 } { \sqrt [ 3 ] { 6 } }$ 
C)  $\frac { 1 } { \sqrt [ 3 ] { 2 } }$ 
D)  $\sqrt [ 3 ] { 2 }$ 
A)  $\sqrt [ 3 ] { 6 }$ 
B)  $\frac { 1 } { \sqrt [ 3 ] { 6 } }$ 
C)  $\frac { 1 } { \sqrt [ 3 ] { 2 } }$ 
D)  $\sqrt [ 3 ] { 2 }$

Question 15

Find the root. Assume that all variables represent nonnegative real numbers.
-$- \sqrt [ 5 ] { 243 }$

Accepted Answer

A)  $- \frac { 243 } { 5 }$ 
B)  3 
C)  $- 3$ 
D)  not a real number 
A)  $- \frac { 243 } { 5 }$ 
B)  3 
C)  $- 3$ 
D)  not a real number

Question 16

Multiply or divide.
-$\sqrt { 4 } \cdot \sqrt { - 1 }$

Accepted Answer

A)  $- 2 \mathrm { i }$ 
B)  $- 2$ 
C)  2 
D)  $2 \mathrm { i }$ 
A)  $- 2 \mathrm { i }$ 
B)  $- 2$ 
C)  2 
D)  $2 \mathrm { i }$

Question 17

Find the root. Assume that all variables represent nonnegative real numbers.
-$$\sqrt [ 3 ] { x ^ { 42 } }$$

Accepted Answer

A)  $x ^ { 14 }$ 
B)  $\sqrt [ 3 ] { \mathrm { x } ^ { 42 } }$ 
C)  $x ^ { 39 }$ 
D)  $x ^ { 21 }$ 
A)  $x ^ { 14 }$ 
B)  $\sqrt [ 3 ] { \mathrm { x } ^ { 42 } }$ 
C)  $x ^ { 39 }$ 
D)  $x ^ { 21 }$

Question 18

Fill in the blank with one of the words or phrases listed below.

-The ــــــــــــof a number a is written as $\sqrt [ 3 ] { a }$.

Accepted Answer

A)  radicand 
B)  principal square root 
C)  index 
D)  cube root 
A)  radicand 
B)  principal square root 
C)  index 
D)  cube root

Question 19

Solve the problem.
-Police use the formula s $= \sqrt { 30 f d }$ to estimate the speed s of a car in miles per hour, where $d$ is the distance in feet that the car skidded and $\mathrm { f }$ is the coefficient of friction. If the coefficient of friction on a certain dry road is $0.84$ and a car was traveling on it at a rate of $40 \mathrm { mph }$, how far will the car skid? Round to the nearest foot.

Accepted Answer

A)  $32 \mathrm { ft }$ 
B)  $53 \mathrm { ft }$ 
C)  $403 \mathrm { ft }$ 
D)  $63 \mathrm { ft }$ 
A)  $32 \mathrm { ft }$ 
B)  $53 \mathrm { ft }$ 
C)  $403 \mathrm { ft }$ 
D)  $63 \mathrm { ft }$

Question 20

Add or subtract. Assume all variables represent positive real numbers.
-$\sqrt { 49 } + \sqrt { 720 } + \sqrt { 100 } + \sqrt { 405 }$

Accepted Answer

A)  $\sqrt { 720 } + \sqrt { 405 } + 17$ 
B)  $21 \sqrt { 5 } + \sqrt { 49 } + \sqrt { 100 }$ 
C)  $225 \sqrt { 5 } + 17$ 
D)  $21 \sqrt { 5 } + 17$ 
A)  $\sqrt { 720 } + \sqrt { 405 } + 17$ 
B)  $21 \sqrt { 5 } + \sqrt { 49 } + \sqrt { 100 }$ 
C)  $225 \sqrt { 5 } + 17$ 
D)  $21 \sqrt { 5 } + 17$

Find the square root. Assume that all variables represent nonnegative real numbers. - $\sqrt { 256 }$

Find the midpoint of the line segment whose endpoints are given. - $( 4,7 ) , ( 8,5 )$

Solve. - $\sqrt { x + 2 } = 2$

Find the midpoint of the line segment whose endpoints are given. - $( - 9 , - 9 ) , ( 2,1 )$

Use rational exponents to write as a single radical expression. - $\frac { \sqrt [ 8 ] { \mathrm { y } } } { \sqrt [ 9 ] { \mathrm { y } } }$

Use radical notation to write the expression. Simplify if possible. - $- \left( \frac { 81 } { 256 } \right) ^ { 1 / 4 }$

Solve. -Find the area of the trapezoid. Simplify if possible.

Write with positive exponents. Simplify if possible. - $\frac { 7 } { 6 x ^ { - 2 / 7 } }$

Solve. -Find the perimeter of the trapezoid. Simplify.

Use the product rule to multiply. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 216 } \cdot \sqrt [ 3 ] { 729 }$

Solve. - $\sqrt { \mathrm { x } } - 2 = \sqrt { \mathrm { x } + 32 }$

Find all real square roots of the number. 1849

Simplify. Assume that all variables represent positive real numbers. - $\frac { \sqrt [ 3 ] { 12 } } { \sqrt [ 3 ] { 6 } }$

Find the root. Assume that all variables represent nonnegative real numbers. - $- \sqrt [ 5 ] { 243 }$

Multiply or divide. - $\sqrt { 4 } \cdot \sqrt { - 1 }$

Find the root. Assume that all variables represent nonnegative real numbers. - $\sqrt [ 3 ] { x ^ { 42 } }$

Fill in the blank with one of the words or phrases listed below. $Fill in the blank with one of the words or phrases listed below. -The ــــــــــــof a number a is written as \sqrt [ 3 ] { a } .$ -The ــــــــــــof a number a is written as $\sqrt [ 3 ] { a }$ .

Add or subtract. Assume all variables represent positive real numbers. - $\sqrt { 49 } + \sqrt { 720 } + \sqrt { 100 } + \sqrt { 405 }$

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Exam 7: Rational Exponents, Radicals, and Complex Numbers

Find the square root. Assume that all variables represent nonnegative real numbers. - 256\sqrt { 256 }256​

Find the midpoint of the line segment whose endpoints are given. - (4,7),(8,5)( 4,7 ) , ( 8,5 )(4,7),(8,5)

Solve. - x+2=2\sqrt { x + 2 } = 2x+2​=2

Find the midpoint of the line segment whose endpoints are given. - (−9,−9),(2,1)( - 9 , - 9 ) , ( 2,1 )(−9,−9),(2,1)

Use rational exponents to write as a single radical expression. - y8y9\frac { \sqrt [ 8 ] { \mathrm { y } } } { \sqrt [ 9 ] { \mathrm { y } } }9y​8y​​

Use radical notation to write the expression. Simplify if possible. - −(81256)1/4- \left( \frac { 81 } { 256 } \right) ^ { 1 / 4 }−(25681​)1/4