Question 1

Find the indicated root, or state that the expression is not a real number.
-$$- \sqrt [ 3 ] { - 125 }$$

Accepted Answer

A)  not a real number 
B)  5 
C)  $- 5$ 
D)  125 
A)  not a real number 
B)  5 
C)  $- 5$ 
D)  125

Question 2

Rewrite the expression with a rational exponent.
-$\sqrt [ 4 ] { 8 }$

Accepted Answer

A)  $8 ^ { 4 }$ 
B)  $\frac { 1 } { 8 ^ { 4 } }$ 
C)  $\frac { 1 } { 4 } \cdot 8$ 
D)  $8 ^ { 1 / 4 }$ 
A)  $8 ^ { 4 }$ 
B)  $\frac { 1 } { 8 ^ { 4 } }$ 
C)  $\frac { 1 } { 4 } \cdot 8$ 
D)  $8 ^ { 1 / 4 }$

Question 3

Find the domain of the square root function. Then use the domain to choose the correct graph of the function.
-$$f ( x ) = \sqrt { 4 - x }$$

Accepted Answer

A)  domain of $f : [ 4 , \infty )$
  
B)  domain of $\mathrm { f } : ( \infty , 4 ]$
  
C)  domain of $f : ( * , - 4 ]$
  
D)  domain of $f : [ - 4 , \infty )$
  
A)  domain of $f : [ 4 , \infty )$
  
B)  domain of $\mathrm { f } : ( \infty , 4 ]$
  
C)  domain of $f : ( * , - 4 ]$
  
D)  domain of $f : [ - 4 , \infty )$

Question 4

Find the indicated function value for the function.
-Evaluate $f ( x ) = - \sqrt [ 3 ] { 64 x - 1 }$ for $f ( 0 )$

Accepted Answer

A)  not a real number 
B)  1 
C)  $- 1$ 
D)  $- 3$ 
A)  not a real number 
B)  1 
C)  $- 1$ 
D)  $- 3$

Question 5

Simplify the expression.
-$$\sqrt { x ^ { 2 } - 14 x + 49 }$$

Accepted Answer

A)  $x + 7$ 
B)  $x - 7$ 
C)  $| ( x - 7 ) ( x + 7 ) |$ 
D)  $| x - 7 |$ 
A)  $x + 7$ 
B)  $x - 7$ 
C)  $| ( x - 7 ) ( x + 7 ) |$ 
D)  $| x - 7 |$

Question 6

Use radical notation to rewrite the expression. Simplify, if possible.
-$$( - 125 ) ^ { 2 / 3 }$$

Accepted Answer

A)  25 
B)  $- \frac { 1 } { 5 }$ 
C)  $- 5$ 
D)  $- 25$ 
A)  25 
B)  $- \frac { 1 } { 5 }$ 
C)  $- 5$ 
D)  $- 25$

Question 7

Find the function value indicated for the function. If necessary, round to two decimal places. If the function value is not a real number and does not exist, state so.
-Evaluate $f ( x ) = \sqrt { x - 25 }$ for $f ( 1 )$

Accepted Answer

A)  $- \sqrt { 24 }$ 
B)  not a real number 
C)  24 
D)  $- 4$ 
A)  $- \sqrt { 24 }$ 
B)  not a real number 
C)  24 
D)  $- 4$

Question 8

Rewrite the expression with a rational exponent.
-$\sqrt [ 7 ] { x y ^ { 2 } }$

Accepted Answer

A)  $\left( x y ^ { 2 } \right) ^ { 7 }$ 
B)  $\left( x y ^ { 2 } \right) ^ { 1 / 7 }$ 
C)  $\frac { 1 } { \left( x y ^ { 2 } \right) ^ { 7 } }$ 
D)  $x ^ { 1 / 7 } y ^ { 2 }$ 
A)  $\left( x y ^ { 2 } \right) ^ { 7 }$ 
B)  $\left( x y ^ { 2 } \right) ^ { 1 / 7 }$ 
C)  $\frac { 1 } { \left( x y ^ { 2 } \right) ^ { 7 } }$ 
D)  $x ^ { 1 / 7 } y ^ { 2 }$

Question 9

Find the indicated root, or state that the expression is not a real number.
-$\sqrt [ 3 ] { - 27 }$

Accepted Answer

A)  $- 3$ 
B)  3 
C)  not a real number 
D)  $- \sqrt [ 3 ] { 3 }$ 
A)  $- 3$ 
B)  3 
C)  not a real number 
D)  $- \sqrt [ 3 ] { 3 }$

Question 10

Use radical notation to rewrite the expression. Simplify, if possible.
-$\left( 2 x y ^ { 4 } \right) ^ { 1 / 5 }$

Accepted Answer

A)  $\sqrt [ 5 ] { 2 x y ^ { 4 } }$ 
B)  $\frac { 1 } { 2 x y ^ { 4 } }$ 
C)  $y \sqrt [ 5 ] { 2 x }$ 
D)  $\frac { 1 } { \sqrt [ 5 ] { 2 x y ^ { 4 } } }$ 
A)  $\sqrt [ 5 ] { 2 x y ^ { 4 } }$ 
B)  $\frac { 1 } { 2 x y ^ { 4 } }$ 
C)  $y \sqrt [ 5 ] { 2 x }$ 
D)  $\frac { 1 } { \sqrt [ 5 ] { 2 x y ^ { 4 } } }$

Question 11

Simplify the expression.
-$$- \sqrt { x ^ { 2 } - 16 x + 64 }$$

Accepted Answer

A)  $- | x - 8 |$ 
B)  $- x + 8$ 
C)  $| x - 8 |$ 
D)  $- x - 8$ 
A)  $- | x - 8 |$ 
B)  $- x + 8$ 
C)  $| x - 8 |$ 
D)  $- x - 8$

Question 12

Solve the problem.
-The formula $\mathrm { v } = \sqrt { 2.5 \mathrm { r } }$ models the safe maximum speed, $\mathrm { v }$, in miles per hour, at which a car can travel on a curved road with radius of curvature, $r$, in feet. A highway crew measures the radius of curvature at an exit ramp as 360 feet. What is the maximum safe speed?

Accepted Answer

A)  30 mph 
B)  36 mph 
C)  27 mph 
D)  35 mph 
A)  30 mph 
B)  36 mph 
C)  27 mph 
D)  35 mph

Question 13

Rewrite the expression with a positive rational exponent. Simplify, if possible.
-$125 ^ { - 1 / 3 }$

Accepted Answer

A)  $- \frac { 1 } { 5 }$ 
B)  $\frac { 1 } { 125 }$ 
C)  $- 5$ 
D)  $\frac { 1 } { 5 }$ 
A)  $- \frac { 1 } { 5 }$ 
B)  $\frac { 1 } { 125 }$ 
C)  $- 5$ 
D)  $\frac { 1 } { 5 }$

Question 14

Use radical notation to rewrite the expression. Simplify, if possible.
-$( x y ) ^ { 8 / 9 }$

Accepted Answer

A)  $\sqrt [ 9 ] { \mathrm { xy } ^ { 8 } }$ 
B)  $\sqrt [ 9 ] { ( x y ) ^ { 8 } }$ 
C)  $\frac { ( x y ) ^ { 8 } } { 9 }$ 
D)  $\sqrt [ 8 ] { ( x y ) ^ { 9 } }$ 
A)  $\sqrt [ 9 ] { \mathrm { xy } ^ { 8 } }$ 
B)  $\sqrt [ 9 ] { ( x y ) ^ { 8 } }$ 
C)  $\frac { ( x y ) ^ { 8 } } { 9 }$ 
D)  $\sqrt [ 8 ] { ( x y ) ^ { 9 } }$

Question 15

Find the cube root.
-$$- \sqrt [ 3 ] { 729 }$$

Accepted Answer

A)  9 
B)  81 
C)  $- 729$ 
D)  $- 9$ 
A)  9 
B)  81 
C)  $- 729$ 
D)  $- 9$

Question 16

Find the indicated root, or state that the expression is not a real number.
-$- \sqrt [ 4 ] { 16 }$

Accepted Answer

A)  not a real number 
B)  $- 2$ 
C)  $- 4$ 
D)  2 
A)  not a real number 
B)  $- 2$ 
C)  $- 4$ 
D)  2

Question 17

Find the indicated root, or state that the expression is not a real number.
-$\sqrt [ 6 ] { - 1 }$

Accepted Answer

A)  1 
B)  $- 1$ 
C)  not a real number 
D)  0 
A)  1 
B)  $- 1$ 
C)  not a real number 
D)  0

Question 18

Rewrite the expression with a rational exponent.
-$\sqrt [ 5 ] { 9 x ^ { 6 } y }$

Accepted Answer

A)  $\frac { 1 } { 5 } \cdot \left( 9 x ^ { 6 } y \right)$ 
B)  $\left( 9 x ^ { 6 } y \right) ^ { 1 / 5 }$ 
C)  $\left( 9 x ^ { 6 } y \right) ^ { 5 }$ 
D)  $\frac { 1 } { \left( 9 x ^ { 6 } y \right) ^ { 5 } }$ 
A)  $\frac { 1 } { 5 } \cdot \left( 9 x ^ { 6 } y \right)$ 
B)  $\left( 9 x ^ { 6 } y \right) ^ { 1 / 5 }$ 
C)  $\left( 9 x ^ { 6 } y \right) ^ { 5 }$ 
D)  $\frac { 1 } { \left( 9 x ^ { 6 } y \right) ^ { 5 } }$

Find the indicated root, or state that the expression is not a real number. - $- \sqrt [ 3 ] { - 125 }$

Rewrite the expression with a rational exponent. - $\sqrt [ 4 ] { 8 }$

Find the domain of the square root function. Then use the domain to choose the correct graph of the function. - $f ( x ) = \sqrt { 4 - x }$

Find the indicated function value for the function. -Evaluate $f ( x ) = - \sqrt [ 3 ] { 64 x - 1 }$ for $f ( 0 )$

Simplify the expression. - $\sqrt { x ^ { 2 } - 14 x + 49 }$

Use radical notation to rewrite the expression. Simplify, if possible. - $( - 125 ) ^ { 2 / 3 }$

Find the function value indicated for the function. If necessary, round to two decimal places. If the function value is not a real number and does not exist, state so. -Evaluate $f ( x ) = \sqrt { x - 25 }$ for $f ( 1 )$

Rewrite the expression with a rational exponent. - $\sqrt [ 7 ] { x y ^ { 2 } }$

Find the indicated root, or state that the expression is not a real number. - $\sqrt [ 3 ] { - 27 }$

Use radical notation to rewrite the expression. Simplify, if possible. - $\left( 2 x y ^ { 4 } \right) ^ { 1 / 5 }$

Simplify the expression. - $- \sqrt { x ^ { 2 } - 16 x + 64 }$

Rewrite the expression with a positive rational exponent. Simplify, if possible. - $125 ^ { - 1 / 3 }$

Use radical notation to rewrite the expression. Simplify, if possible. - $( x y ) ^ { 8 / 9 }$

Find the cube root. - $- \sqrt [ 3 ] { 729 }$

Find the indicated root, or state that the expression is not a real number. - $- \sqrt [ 4 ] { 16 }$

Find the indicated root, or state that the expression is not a real number. - $\sqrt [ 6 ] { - 1 }$

Rewrite the expression with a rational exponent. - $\sqrt [ 5 ] { 9 x ^ { 6 } y }$

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Exam 7: Radicals, Radical Functions, and Rational Exponents

Find the indicated root, or state that the expression is not a real number. - −−1253- \sqrt [ 3 ] { - 125 }−3−125​

Rewrite the expression with a rational exponent. - 84\sqrt [ 4 ] { 8 }48​

Find the domain of the square root function. Then use the domain to choose the correct graph of the function. - f(x)=4−xf ( x ) = \sqrt { 4 - x }f(x)=4−x​

Find the indicated function value for the function. -Evaluate f(x)=−64x−13f ( x ) = - \sqrt [ 3 ] { 64 x - 1 }f(x)=−364x−1​ for f(0)f ( 0 )f(0)

Simplify the expression. - x2−14x+49\sqrt { x ^ { 2 } - 14 x + 49 }x2−14x+49​

Use radical notation to rewrite the expression. Simplify, if possible. - (−125)2/3( - 125 ) ^ { 2 / 3 }(−125)2/3

Find the function value indicated for the function. If necessary, round to two decimal places. If the function value is not a real number and does not exist, state so. -Evaluate f(x)=x−25f ( x ) = \sqrt { x - 25 }f(x)=x−25​ for f(1)f ( 1 )f(1)

Rewrite the expression with a rational exponent. - xy27\sqrt [ 7 ] { x y ^ { 2 } }7xy2​

Find the indicated root, or state that the expression is not a real number. - −273\sqrt [ 3 ] { - 27 }3−27​

Use radical notation to rewrite the expression. Simplify, if possible. - (2xy4)1/5\left( 2 x y ^ { 4 } \right) ^ { 1 / 5 }(2xy4)1/5

Simplify the expression. - −x2−16x+64- \sqrt { x ^ { 2 } - 16 x + 64 }−x2−16x+64​

Rewrite the expression with a positive rational exponent. Simplify, if possible. - 125−1/3125 ^ { - 1 / 3 }125−1/3

Use radical notation to rewrite the expression. Simplify, if possible. - (xy)8/9( x y ) ^ { 8 / 9 }(xy)8/9

Find the cube root. - −7293- \sqrt [ 3 ] { 729 }−3729​

Find the indicated root, or state that the expression is not a real number. - −164- \sqrt [ 4 ] { 16 }−416​

Find the indicated root, or state that the expression is not a real number. - −16\sqrt [ 6 ] { - 1 }6−1​

Rewrite the expression with a rational exponent. - 9x6y5\sqrt [ 5 ] { 9 x ^ { 6 } y }59x6y​