Question 1

Use radical notation to rewrite the expression. Simplify, if possible.
-$- 16 ^ { 1 / 4 }$

Accepted Answer

A)  $- \sqrt [ 4 ] { 2 }$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $- 2$ 
D)  2 
A)  $- \sqrt [ 4 ] { 2 }$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $- 2$ 
D)  2 C

Question 2

Find the square root if it is a real number, or state that the expression is not a real number.
-$\sqrt { 100 - 200 }$

Accepted Answer

A)  $- 100$ 
B)  10 
C)  not a real number 
D)  $- 10$ 
A)  $- 100$ 
B)  10 
C)  not a real number 
D)  $- 10$ C

Question 3

Find the cube root.
-$\sqrt [ 3 ] { \frac { 1 } { 64 } }$

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  4 
C)  $\frac { 1 } { \sqrt [ 3 ] { 4 } }$ 
D)  $\frac { 1 } { 16 }$ 
A)  $\frac { 1 } { 4 }$ 
B)  4 
C)  $\frac { 1 } { \sqrt [ 3 ] { 4 } }$ 
D)  $\frac { 1 } { 16 }$ A

Question 4

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
-$\frac { x ^ { 1 / 3 } } { x ^ { 6 / 7 } }$

Accepted Answer

A)  $\frac { 1 } { \mathrm { x } ^ { 11 / 21 } }$ 
B)  $x ^ { 25 / 21 }$ 
C)  $x ^ { 7 / 18 }$ 
D)  $x ^ { 11 / 21 }$ 
A)  $\frac { 1 } { \mathrm { x } ^ { 11 / 21 } }$ 
B)  $x ^ { 25 / 21 }$ 
C)  $x ^ { 7 / 18 }$ 
D)  $x ^ { 11 / 21 }$

Question 5

Simplify the expression.
-$- \sqrt { 49 x ^ { 8 } }$

Accepted Answer

A)  $\left| 7 x ^ { 4 } \right|$ 
B)  $- \left| 49 x ^ { 4 } \right|$ 
C)  $- 7 x ^ { 8 }$ 
D)  $- \left| 7 x ^ { 4 } \right|$ 
A)  $\left| 7 x ^ { 4 } \right|$ 
B)  $- \left| 49 x ^ { 4 } \right|$ 
C)  $- 7 x ^ { 8 }$ 
D)  $- \left| 7 x ^ { 4 } \right|$

Question 6

Find the square root if it is a real number, or state that the expression is not a real number.
-$$\sqrt { 144 + 25 }$$

Accepted Answer

A)  $\sqrt { 119 }$ 
B)  13 
C)  169 
D)  17 
A)  $\sqrt { 119 }$ 
B)  13 
C)  169 
D)  17

Question 7

Find the square root if it is a real number, or state that the expression is not a real number.
-$\sqrt { \frac { 1 } { 81 } }$

Accepted Answer

A)  9 
B)  $\frac { 1 } { 9 }$ 
C)  $\frac { 1 } { 6561 }$ 
D)  81 
A)  9 
B)  $\frac { 1 } { 9 }$ 
C)  $\frac { 1 } { 6561 }$ 
D)  81

Question 8

Rewrite the expression with a rational exponent.
-$\sqrt { 6 }$

Accepted Answer

A)  $\frac { 1 } { 6 ^ { 2 } }$ 
B)  $6 ^ { 1 / 2 }$ 
C)  $6 ^ { 2 }$ 
D)  $\frac { 1 } { 2 } \cdot 6$ 
A)  $\frac { 1 } { 6 ^ { 2 } }$ 
B)  $6 ^ { 1 / 2 }$ 
C)  $6 ^ { 2 }$ 
D)  $\frac { 1 } { 2 } \cdot 6$

Question 9

Find the indicated root, or state that the expression is not a real number.
-$\sqrt [ 4 ] { 81 }$

Accepted Answer

A)  9 
B)  12 
C)  3 
D)  $- 3$ 
A)  9 
B)  12 
C)  3 
D)  $- 3$

Question 10

Find the square root if it is a real number, or state that the expression is not a real number.
-$- \sqrt { 36 }$

Accepted Answer

A)  $- 18$ 
B)  not a real number 
C)  6 
D)  $- 6$ 
A)  $- 18$ 
B)  not a real number 
C)  6 
D)  $- 6$

Question 11

Solve.
-The function $\mathrm { f } ( \mathrm { x } ) = 0.07 \mathrm { x } ^ { 3 / 2 }$ models the duration of a storm, $\mathrm { f } ( \mathrm { x } )$, in hours, in terms of the diameter of the storm, $x$, in miles. Use a calculator to determine the duration of a storm with a diameter of 12 miles. Round to the nearest hundredth.

Accepted Answer

A)  $41.57 \mathrm { hr }$ 
B)  $0.77 \mathrm { hr }$ 
C)  $2.91 \mathrm { hr }$ 
D)  $0.24 \mathrm { hr }$ 
A)  $41.57 \mathrm { hr }$ 
B)  $0.77 \mathrm { hr }$ 
C)  $2.91 \mathrm { hr }$ 
D)  $0.24 \mathrm { hr }$

Question 12

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.
-$$\text { Evaluate } c ( x ) = \sqrt { x + 6 } \text { for } c ( - 2 )$$

Accepted Answer

A)  2 
B)  not a real number 
C)  -2 
D)  1.41 
A)  2 
B)  not a real number 
C)  -2 
D)  1.41

Question 13

Find the indicated root, or state that the expression is not a real number.
-$- \sqrt [ 3 ] { 8 }$

Accepted Answer

A)  $- 2$ 
B)  2 
C)  $- \sqrt [ 3 ] { 2 }$ 
D)  not a real number 
A)  $- 2$ 
B)  2 
C)  $- \sqrt [ 3 ] { 2 }$ 
D)  not a real number

Question 14

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

Accepted Answer

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

Question 15

Find the domain of the square root function. Then use the domain to choose the correct graph of the function.
-$$f ( x ) = \sqrt { 64 - 8 x }$$

Accepted Answer

A)  domain of $f : [ 8 , \infty )$
  
B)  domain of $\mathrm { f } : [ - 8 , \infty )$
  
C)  domain of $f : ( \infty , - 8 ]$
  
D)  domain of $\mathrm { f } : ( \infty , 8 ]$
  
A)  domain of $f : [ 8 , \infty )$
  
B)  domain of $\mathrm { f } : [ - 8 , \infty )$
  
C)  domain of $f : ( \infty , - 8 ]$
  
D)  domain of $\mathrm { f } : ( \infty , 8 ]$

Question 16

Simplify the expression. Include absolute value bars where necessary.
-$\sqrt [ 3 ] { - 64 x ^ { 3 } }$

Accepted Answer

A)  $4 x$ 
B)  $- | - 4 | x$ 
C)  $| - 4 | x$ 
D)  $- 4 x$ 
A)  $4 x$ 
B)  $- | - 4 | x$ 
C)  $| - 4 | x$ 
D)  $- 4 x$

Question 17

Find the indicated function value for the function.
-$$\text { Evaluate } \mathrm { f } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } + 7 } \text { for } \mathrm { f } ( 118 )$$

Accepted Answer

A)  5 
B)  5, -5 
C)  12 
D)  125 
A)  5 
B)  5, -5 
C)  12 
D)  125

Question 18

Simplify the expression.
-$\sqrt { ( - 5 ) ^ { 2 } }$

Accepted Answer

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

Question 19

Find the indicated function value for the function.
-$$\text { Evaluate } f ( x ) = \sqrt [ 3 ] { x + 3 } \text { for } f ( - 11 )$$

Accepted Answer

A)  2 
B)  -8 
C)  -2 
D)  not a real number 
A)  2 
B)  -8 
C)  -2 
D)  not a real number

Question 20

Simplify the expression. Include absolute value bars where necessary.
-$$\sqrt [ 6 ] { ( x + 2 ) ^ { 6 } }$$

Accepted Answer

A)  $| x + 2 |$ 
B)  $| x | + 2$ 
C)  $\pm x + 2$ 
D)  $x + 2$ 
A)  $| x + 2 |$ 
B)  $| x | + 2$ 
C)  $\pm x + 2$ 
D)  $x + 2$

Use radical notation to rewrite the expression. Simplify, if possible. - $- 16 ^ { 1 / 4 }$

Find the square root if it is a real number, or state that the expression is not a real number. - $\sqrt { 100 - 200 }$

Find the cube root. - $\sqrt [ 3 ] { \frac { 1 } { 64 } }$

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. - $\frac { x ^ { 1 / 3 } } { x ^ { 6 / 7 } }$

Simplify the expression. - $- \sqrt { 49 x ^ { 8 } }$

Find the square root if it is a real number, or state that the expression is not a real number. - $\sqrt { 144 + 25 }$

Find the square root if it is a real number, or state that the expression is not a real number. - $\sqrt { \frac { 1 } { 81 } }$

Rewrite the expression with a rational exponent. - $\sqrt { 6 }$

Find the indicated root, or state that the expression is not a real number. - $\sqrt [ 4 ] { 81 }$

Find the square root if it is a real number, or state that the expression is not a real number. - $- \sqrt { 36 }$

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. - $\text { Evaluate } c ( x ) = \sqrt { x + 6 } \text { for } c ( - 2 )$

Find the indicated root, or state that the expression is not a real number. - $- \sqrt [ 3 ] { 8 }$

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

Find the domain of the square root function. Then use the domain to choose the correct graph of the function. - $f ( x ) = \sqrt { 64 - 8 x }$

Simplify the expression. Include absolute value bars where necessary. - $\sqrt [ 3 ] { - 64 x ^ { 3 } }$

Find the indicated function value for the function. - $\text { Evaluate } \mathrm { f } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } + 7 } \text { for } \mathrm { f } ( 118 )$

Simplify the expression. - $\sqrt { ( - 5 ) ^ { 2 } }$

Find the indicated function value for the function. - $\text { Evaluate } f ( x ) = \sqrt [ 3 ] { x + 3 } \text { for } f ( - 11 )$

Simplify the expression. Include absolute value bars where necessary. - $\sqrt [ 6 ] { ( x + 2 ) ^ { 6 } }$

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Exam 7: Radicals, Radical Functions, and Rational Exponents

Use radical notation to rewrite the expression. Simplify, if possible. - −161/4- 16 ^ { 1 / 4 }−161/4

Find the square root if it is a real number, or state that the expression is not a real number. - 100−200\sqrt { 100 - 200 }100−200​

Find the cube root. - 1643\sqrt [ 3 ] { \frac { 1 } { 64 } }3641​​

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. - x1/3x6/7\frac { x ^ { 1 / 3 } } { x ^ { 6 / 7 } }x6/7x1/3​

Simplify the expression. - −49x8- \sqrt { 49 x ^ { 8 } }−49x8​

Find the square root if it is a real number, or state that the expression is not a real number. - 144+25\sqrt { 144 + 25 }144+25​

Find the square root if it is a real number, or state that the expression is not a real number. - 181\sqrt { \frac { 1 } { 81 } }811​​

Rewrite the expression with a rational exponent. - 6\sqrt { 6 }6​

Find the indicated root, or state that the expression is not a real number. - 814\sqrt [ 4 ] { 81 }481​

Find the square root if it is a real number, or state that the expression is not a real number. - −36- \sqrt { 36 }−36​

Find the indicated root, or state that the expression is not a real number. - −83- \sqrt [ 3 ] { 8 }−38​

Use radical notation to rewrite the expression. Simplify, if possible. - (xy)1/5( x y ) ^ { 1 / 5 }(xy)1/5

Find the domain of the square root function. Then use the domain to choose the correct graph of the function. - f(x)=64−8xf ( x ) = \sqrt { 64 - 8 x }f(x)=64−8x​

Simplify the expression. Include absolute value bars where necessary. - −64x33\sqrt [ 3 ] { - 64 x ^ { 3 } }3−64x3​

Find the indicated function value for the function. - Evaluate f(x)=x+73 for f(118)\text { Evaluate } \mathrm { f } ( \mathrm { x } ) = \sqrt [ 3 ] { \mathrm { x } + 7 } \text { for } \mathrm { f } ( 118 ) Evaluate f(x)=3x+7​ for f(118)

Simplify the expression. - (−5)2\sqrt { ( - 5 ) ^ { 2 } }(−5)2​

Find the indicated function value for the function. - Evaluate f(x)=x+33 for f(−11)\text { Evaluate } f ( x ) = \sqrt [ 3 ] { x + 3 } \text { for } f ( - 11 ) Evaluate f(x)=3x+3​ for f(−11)

Simplify the expression. Include absolute value bars where necessary. - (x+2)66\sqrt [ 6 ] { ( x + 2 ) ^ { 6 } }6(x+2)6​