Question 1

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

Accepted Answer

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

Question 2

Rewrite the expression with a rational exponent.
-$\sqrt [ 3 ] { 45 }$

Accepted Answer

A)  $\frac { 1 } { 3 } \cdot 45$ 
B)  $45 ^ { 3 }$ 
C)  $\frac { 1 } { 45 ^ { 3 } }$ 
D)  $45 ^ { 1 / 3 }$ 
A)  $\frac { 1 } { 3 } \cdot 45$ 
B)  $45 ^ { 3 }$ 
C)  $\frac { 1 } { 45 ^ { 3 } }$ 
D)  $45 ^ { 1 / 3 }$

Question 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.
-$z ( x ) = \sqrt { ( x + 7 ) ^ { 2 } }$ for $z ( - 3 )$

Accepted Answer

A)  16 
B)  4 
C)  not a real number 
D)  58 
A)  16 
B)  4 
C)  not a real number 
D)  58

Question 4

Rewrite the expression with a rational exponent.
-$( \sqrt { 6 x y } ) ^ { 3 }$

Accepted Answer

A)  $\frac { ( 6 x y ) ^ { 3 } } { 2 }$ 
B)  $( 6 x y ) ^ { 3 / 2 }$ 
C)  $\frac { ( 6 x y ) ^ { 2 } } { 3 }$ 
D)  $( 6 x y ) ^ { 2 / 3 }$ 
A)  $\frac { ( 6 x y ) ^ { 3 } } { 2 }$ 
B)  $( 6 x y ) ^ { 3 / 2 }$ 
C)  $\frac { ( 6 x y ) ^ { 2 } } { 3 }$ 
D)  $( 6 x y ) ^ { 2 / 3 }$

Question 5

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.
-$$\text { Evaluate } f ( x ) = \sqrt { - x + 34 } \text { for } f ( - 2 )$$

Accepted Answer

A)  6 
B)  2.45 
C)  not a real number 
D)  5.66 
A)  6 
B)  2.45 
C)  not a real number 
D)  5.66

Question 6

Find the domain of the square root function. Then use the domain to choose the correct graph of the function.
-$$f ( x ) = \sqrt { 9 x - 36 }$$

Accepted Answer

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

Question 7

Simplify the expression. Include absolute value bars where necessary.
-$\sqrt [ 8 ] { x ^ { 8 } }$

Accepted Answer

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

Question 8

Find the indicated root, or state that the expression is not a real number.
-$$\sqrt [ 4 ] { - 256 }$$

Accepted Answer

A)  not a real number 
B)  -16 
C)  -4 
D)  4 
A)  not a real number 
B)  -16 
C)  -4 
D)  4

Question 9

Use radical notation to rewrite the expression. Simplify, if possible.
-$$16 ^ { 3 / 4 } + 64 ^ { 2 / 3 }$$

Accepted Answer

A)  $113 \frac { 1 } { 3 }$ 
B)  24 
C)  25 
D)  $54 \frac { 2 } { 3 }$ 
A)  $113 \frac { 1 } { 3 }$ 
B)  24 
C)  25 
D)  $54 \frac { 2 } { 3 }$

Question 10

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers.
-$\left( 64 x ^ { 4 } y ^ { 4 } \right) ^ { 1 / 2 }$

Accepted Answer

A)  $32 x ^ { 2 } y ^ { 2 }$ 
B)  $8 x ^ { 7 / 2 } y = / 2$ 
C)  $8 \mathrm { x } ^ { 2 } \mathrm { y } ^ { 2 }$ 
D)  $8 x ^ { 9 / 2 } y ^ { 9 / 2 }$ 
A)  $32 x ^ { 2 } y ^ { 2 }$ 
B)  $8 x ^ { 7 / 2 } y = / 2$ 
C)  $8 \mathrm { x } ^ { 2 } \mathrm { y } ^ { 2 }$ 
D)  $8 x ^ { 9 / 2 } y ^ { 9 / 2 }$

Question 11

Simplify the expression. Include absolute value bars where necessary.
-$\sqrt [ 7 ] { g ^ { 7 } }$

Accepted Answer

A)  $\mathrm { g }$ 
B)  $- g$ 
C)  $\sqrt [ 7 ] { \mathrm { g } }$ 
D)  $g ^ { 7 }$ 
A)  $\mathrm { g }$ 
B)  $- g$ 
C)  $\sqrt [ 7 ] { \mathrm { g } }$ 
D)  $g ^ { 7 }$

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.
-Evaluate $m ( x ) = - \sqrt { x - 2 }$ for $m ( 27 )$

Accepted Answer

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

Question 13

Find the indicated root, or state that the expression is not a real number.
-$$- \sqrt [ 4 ] { - 256 }$$

Accepted Answer

A)  not a real number 
B)  $- 4$ 
C)  $- 16$ 
D)  4 
A)  not a real number 
B)  $- 4$ 
C)  $- 16$ 
D)  4

Question 14

Find the indicated function value for the function.
-$$\text { Evaluate } f ( x ) = \sqrt [ 3 ] { x - 27 } \text { for } f ( 0 )$$

Accepted Answer

A)  3 
B)  not a real number 
C)  -3 
D)  0 
A)  3 
B)  not a real number 
C)  -3 
D)  0

Question 15

Simplify the expression. Include absolute value bars where necessary.
-$$\sqrt [ 4 ] { ( x + 81 ) ^ { 4 } }$$

Accepted Answer

A)  $| x + 3 |$ 
B)  $x + 3$ 
C)  $x + 81$ 
D)  $| x + 81 |$ 
A)  $| x + 3 |$ 
B)  $x + 3$ 
C)  $x + 81$ 
D)  $| x + 81 |$

Question 16

Find the cube root.
-$$\sqrt [ 3 ] { - 8 }$$

Accepted Answer

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

Question 17

Simplify the expression. Include absolute value bars where necessary.
-$\sqrt [ 3 ] { - 8 ( x - 3 ) ^ { 3 } }$

Accepted Answer

A)  $- 2 x + 6$ 
B)  $- 2 x - 6$ 
C)  $- 8 x - 3$ 
D)  $| - 2 x + 6 |$ 
A)  $- 2 x + 6$ 
B)  $- 2 x - 6$ 
C)  $- 8 x - 3$ 
D)  $| - 2 x + 6 |$

Question 18

Solve the problem.
-The formula $\mathrm { v } = \sqrt { 20 \mathrm {~L} }$ can be used to estimate the speed of a car, $\mathrm { v }$, in miles per hour, based on the length, L, in feet, of its skid marks upon sudden braking on a dry asphalt road. If a car is involved in an accident and its skid marks measure 45 feet, at what estimated speed was the car traveling when it applied its brakes just prior to the accident?

Accepted Answer

A)  25 mph 
B)  40 mph 
C)  30 mph 
D)  35 mph 
A)  25 mph 
B)  40 mph 
C)  30 mph 
D)  35 mph

Question 19

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 $g ( x ) = \sqrt { x - 5 }$ for $g ( 30 )$

Accepted Answer

A)  5 
B)  not a real number 
C)  $3.24$ 
D)  $5.48 \mathrm {~g}$ 
A)  5 
B)  not a real number 
C)  $3.24$ 
D)  $5.48 \mathrm {~g}$

Question 20

Find the domain of the square root function. Then use the domain to choose the correct graph of the function.
-$$f ( x ) = \sqrt { x + 3 }$$

Accepted Answer

A)  domain of $f : [ - 3 , \infty )$
  
B)  domain of $f : [ 3 , \infty )$
  
C)  domain of $\mathrm { f } : ( \infty , - 3 ]$
  
D)  domain of $\mathrm { f } : ( \infty , 3 ]$
  
A)  domain of $f : [ - 3 , \infty )$
  
B)  domain of $f : [ 3 , \infty )$
  
C)  domain of $\mathrm { f } : ( \infty , - 3 ]$
  
D)  domain of $\mathrm { f } : ( \infty , 3 ]$

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

Rewrite the expression with a rational exponent. - $\sqrt [ 3 ] { 45 }$

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. - $z ( x ) = \sqrt { ( x + 7 ) ^ { 2 } }$ for $z ( - 3 )$

Rewrite the expression with a rational exponent. - $( \sqrt { 6 x y } ) ^ { 3 }$

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. - $\text { Evaluate } f ( x ) = \sqrt { - x + 34 } \text { for } f ( - 2 )$

Find the domain of the square root function. Then use the domain to choose the correct graph of the function. - $f ( x ) = \sqrt { 9 x - 36 }$

Simplify the expression. Include absolute value bars where necessary. - $\sqrt [ 8 ] { x ^ { 8 } }$

Find the indicated root, or state that the expression is not a real number. - $\sqrt [ 4 ] { - 256 }$

Use radical notation to rewrite the expression. Simplify, if possible. - $16 ^ { 3 / 4 } + 64 ^ { 2 / 3 }$

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. - $\left( 64 x ^ { 4 } y ^ { 4 } \right) ^ { 1 / 2 }$

Simplify the expression. Include absolute value bars where necessary. - $\sqrt [ 7 ] { g ^ { 7 } }$

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 $m ( x ) = - \sqrt { x - 2 }$ for $m ( 27 )$

Find the indicated root, or state that the expression is not a real number. - $- \sqrt [ 4 ] { - 256 }$

Find the indicated function value for the function. - $\text { Evaluate } f ( x ) = \sqrt [ 3 ] { x - 27 } \text { for } f ( 0 )$

Simplify the expression. Include absolute value bars where necessary. - $\sqrt [ 4 ] { ( x + 81 ) ^ { 4 } }$

Find the cube root. - $\sqrt [ 3 ] { - 8 }$

Simplify the expression. Include absolute value bars where necessary. - $\sqrt [ 3 ] { - 8 ( x - 3 ) ^ { 3 } }$

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 $g ( x ) = \sqrt { x - 5 }$ for $g ( 30 )$

Find the domain of the square root function. Then use the domain to choose the correct graph of the function. - $f ( x ) = \sqrt { x + 3 }$

Algebra, Mathematical Models, and Problem Solving

Functions and Linear Functions

Systems of Linear Equations

Inequalities and Problem Solving

Polynomials, Polynomial Functions, and Factoring

Rational Expressions, Functions, and Equations

Quadratic Equations and Functions

Filters

Exam 7: Radicals, Radical Functions, and Rational Exponents

Use radical notation to rewrite the expression. Simplify, if possible. - 161/416 ^ { 1 / 4 }161/4

Rewrite the expression with a rational exponent. - 453\sqrt [ 3 ] { 45 }345​

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. - z(x)=(x+7)2z ( x ) = \sqrt { ( x + 7 ) ^ { 2 } }z(x)=(x+7)2​ for z(−3)z ( - 3 )z(−3)

Rewrite the expression with a rational exponent. - (6xy)3( \sqrt { 6 x y } ) ^ { 3 }(6xy​)3

Find the domain of the square root function. Then use the domain to choose the correct graph of the function. - f(x)=9x−36f ( x ) = \sqrt { 9 x - 36 }f(x)=9x−36​

Simplify the expression. Include absolute value bars where necessary. - x88\sqrt [ 8 ] { x ^ { 8 } }8x8​

Find the indicated root, or state that the expression is not a real number. - −2564\sqrt [ 4 ] { - 256 }4−256​

Use radical notation to rewrite the expression. Simplify, if possible. - 163/4+642/316 ^ { 3 / 4 } + 64 ^ { 2 / 3 }163/4+642/3

Use properties of rational exponents to simplify the expression. Assume that any variables represent positive numbers. - (64x4y4)1/2\left( 64 x ^ { 4 } y ^ { 4 } \right) ^ { 1 / 2 }(64x4y4)1/2

Simplify the expression. Include absolute value bars where necessary. - g77\sqrt [ 7 ] { g ^ { 7 } }7g7​

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 m(x)=−x−2m ( x ) = - \sqrt { x - 2 }m(x)=−x−2​ for m(27)m ( 27 )m(27)

Find the indicated root, or state that the expression is not a real number. - −−2564- \sqrt [ 4 ] { - 256 }−4−256​

Find the indicated function value for the function. - Evaluate f(x)=x−273 for f(0)\text { Evaluate } f ( x ) = \sqrt [ 3 ] { x - 27 } \text { for } f ( 0 ) Evaluate f(x)=3x−27​ for f(0)

Simplify the expression. Include absolute value bars where necessary. - (x+81)44\sqrt [ 4 ] { ( x + 81 ) ^ { 4 } }4(x+81)4​

Find the cube root. - −83\sqrt [ 3 ] { - 8 }3−8​

Simplify the expression. Include absolute value bars where necessary. - −8(x−3)33\sqrt [ 3 ] { - 8 ( x - 3 ) ^ { 3 } }3−8(x−3)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 g(x)=x−5g ( x ) = \sqrt { x - 5 }g(x)=x−5​ for g(30)g ( 30 )g(30)

Find the domain of the square root function. Then use the domain to choose the correct graph of the function. - f(x)=x+3f ( x ) = \sqrt { x + 3 }f(x)=x+3​