Question 1

Evaluate if possible. If the expression is not a real number, so state.
-$32^{4 / 5}$

Accepted Answer

A) 16 
B) 256 
C) 512 
D) 128 
A) 16 
B) 256 
C) 512 
D) 128

Question 2

Simplify.
-$3 \sqrt [ 3 ] { x ^ { 3 } y ^ { 13 } } + 2 x y \sqrt [ 3 ] { 27 y ^ { 10 } }$

Accepted Answer

A)  $9 x y ^ { 4 } \sqrt [ 3 ] { y }$ 
B)  $5 x y ^ { 5 } \sqrt [ 3 ] { 27 y }$ 
C)  $5 x ^ { 2 } y ^ { 5 } \sqrt [ 3 ] { y }$ 
D)  $9 x ^ { 2 } y ^ { 4 } \sqrt [ 3 ] { 3 y }$ 
A)  $9 x y ^ { 4 } \sqrt [ 3 ] { y }$ 
B)  $5 x y ^ { 5 } \sqrt [ 3 ] { 27 y }$ 
C)  $5 x ^ { 2 } y ^ { 5 } \sqrt [ 3 ] { y }$ 
D)  $9 x ^ { 2 } y ^ { 4 } \sqrt [ 3 ] { 3 y }$

Question 3

Find the indicated value of the function. Use your calculator to approximate irrational numbers. Round irrational
numbers to the nearest thousandth.
-$\text { Find } f ( 0 ) \text { if } f ( x ) = \sqrt { x ^ { 2 } + 7 x }$

Accepted Answer

A) 7 
B) 2.646 
C) 7.483 
D) 0 
A) 7 
B) 2.646 
C) 7.483 
D) 0

Question 4

Evaluate if possible. If the expression is not a real number, so state.
-$8 ^ { 4 / 3 }$

Accepted Answer

A) 16 
B) 32 
C) 64 
D) 128 
A) 16 
B) 32 
C) 64 
D) 128

Question 5

Simplify.
-$\sqrt [ 3 ] { 16 } + \sqrt [ 3 ] { 128 }$

Accepted Answer

A)  $\sqrt [ 3 ] { 16 }$ 
B)  $6 \sqrt [ 3 ] { 2 }$ 
C) 6 
D)  $12 \sqrt [ 3 ] { 2 }$ 
A)  $\sqrt [ 3 ] { 16 }$ 
B)  $6 \sqrt [ 3 ] { 2 }$ 
C) 6 
D)  $12 \sqrt [ 3 ] { 2 }$

Question 6

Simplify. Write the answer in exponential form without negative exponents.
-$\left( x ^ { - 1 / 2 } \right) ^ { - 1 / 6 }$

Accepted Answer

A)  $x ^ { 12 }$ 
B)  $\frac { 1 } { x ^ { 12 } }$ 
C)  $x ^ { 1 / 12 }$ 
D)  $\frac { 1 } { \mathrm { x } ^ { 1 / 12 } }$ 
A)  $x ^ { 12 }$ 
B)  $\frac { 1 } { x ^ { 12 } }$ 
C)  $x ^ { 1 / 12 }$ 
D)  $\frac { 1 } { \mathrm { x } ^ { 1 / 12 } }$

Question 7

Write as an absolute value.
-$\sqrt { z ^ { 2 } - 12 z + 36 }$

Accepted Answer

A) z + 6 
B)  $$\left| z ^ { 2 } - 12 z + 36 \right|$$ 
C)  $| z - 6 |$ 
D) z - 6 
A) z + 6 
B)  $$\left| z ^ { 2 } - 12 z + 36 \right|$$ 
C)  $| z - 6 |$ 
D) z - 6

Question 8

Solve and check your solution(s). If the equation has no real solution, so state.
-$\sqrt [ 3 ] { 3 - 3 x } = 2$

Accepted Answer

A)  $- \frac { 5 } { 3 }$ 
B)  $- \frac { 7 } { 3 }$ 
C)  $- \frac { 1 } { 3 }$ 
D) no real solution 
A)  $- \frac { 5 } { 3 }$ 
B)  $- \frac { 7 } { 3 }$ 
C)  $- \frac { 1 } { 3 }$ 
D) no real solution

Question 9

Solve and check your solution(s). If the equation has no real solution, so state.
-$\sqrt { x + 9 } = \sqrt { x - 9 }$

Accepted Answer

A) 18 
B) -18 
C) 0 
D) no real solution 
A) 18 
B) -18 
C) 0 
D) no real solution

Question 10

Simplify.
-$( \sqrt { 8 } + \sqrt { z } ) ( \sqrt { 8 } - \sqrt { z } )$

Accepted Answer

A)  $8 - z$ 
B)  $8 - 2 \sqrt { 8 z }$ 
C)  $8 - 2 \sqrt { z }$ 
D)  $8 z$ 
A)  $8 - z$ 
B)  $8 - 2 \sqrt { 8 z }$ 
C)  $8 - 2 \sqrt { z }$ 
D)  $8 z$

Question 11

Solve and check your solution(s). If the equation has no real solution, so state.
-$$\sqrt [ 4 ] { x + 7 } = \sqrt [ 4 ] { 5 x }$$

Accepted Answer

A)  $\frac { 4 } { 7 }$ 
B)  $\frac { 7 } { 4 }$ 
C) 75 
D) no real solution 
A)  $\frac { 4 } { 7 }$ 
B)  $\frac { 7 } { 4 }$ 
C) 75 
D) no real solution

Question 12

Solve the problem.
-A formula used to determine the velocity v in feet per second per second of an object (neglecting air resistance) after it has fallen a certain height iss v $\mathrm { v } = \sqrt { 2 \mathrm { gh } },$ , where g is the acceler where g is the acceleation due to gravity and h is the height the
Object has fallen. If the acceleration g due to gravity on Earth is approximately 32 feet per second per second,
Find the velocity of a bowling ball after it has fallen 30 feet. (Round to the nearest tenth.)

Accepted Answer

A) 31.0 ft/sec 
B) 43.8 ft/sec 
C) 1920 ft/sec 
D) 7.7 ft/sec 
A) 31.0 ft/sec 
B) 43.8 ft/sec 
C) 1920 ft/sec 
D) 7.7 ft/sec

Question 13

Simplify.
-$\sqrt { \frac { 100 } { 9 } }$

Accepted Answer

A)  $\frac { 10 } { 3 }$ 
B)  $\frac { \sqrt { 10 } } { 3 }$ 
C) 3 
D)  $\frac { \sqrt { 10 } } { \sqrt { 3 } }$ 
A)  $\frac { 10 } { 3 }$ 
B)  $\frac { \sqrt { 10 } } { 3 }$ 
C) 3 
D)  $\frac { \sqrt { 10 } } { \sqrt { 3 } }$

Question 14

Multiply. Write the result in the form a + bi.
-$( 2 + \sqrt { - 2 } ) ( 4 + \sqrt { - 2 } )$

Accepted Answer

A)  $( 8 - \sqrt { 4 } ) + ( 2 \sqrt { 2 } + 4 \sqrt { 2 } ) \mathrm { i }$ 
B)  $4 - 6 \sqrt { 4 } i$ 
C)  $( 8 + \sqrt { 4 } ) - 12 i$ 
D)  $12 + 24 \mathrm { i }$ 
A)  $( 8 - \sqrt { 4 } ) + ( 2 \sqrt { 2 } + 4 \sqrt { 2 } ) \mathrm { i }$ 
B)  $4 - 6 \sqrt { 4 } i$ 
C)  $( 8 + \sqrt { 4 } ) - 12 i$ 
D)  $12 + 24 \mathrm { i }$

Question 15

Simplify. Write the answer in exponential form without negative exponents.
-$\frac { x ^ { 3 } } { x ^ { - 1 / 5 } }$

Accepted Answer

A)  $x ^ { 3 / 5 }$ 
B)  $x ^ { 14 / 5 }$ 
C)  $x ^ { 16 / 5 }$ 
D)  $\frac { 1 } { x ^ { 3 / 5 } }$ 
A)  $x ^ { 3 / 5 }$ 
B)  $x ^ { 14 / 5 }$ 
C)  $x ^ { 16 / 5 }$ 
D)  $\frac { 1 } { x ^ { 3 / 5 } }$

Question 16

Simplify.
-$\left( \sqrt [ 3 ] { 5 x ^ { 12 } y ^ { 16 } } \right) ^ { 2 }$

Accepted Answer

A)  $x ^ { 8 } y ^ { 10 } \sqrt [ 3 ] { 25 y ^ { 2 } }$ 
B)  $x ^ { 8 } y ^ { 10 } \sqrt [ 3 ] { 5 y ^ { 2 } }$ 
C)  $x ^ { 8 } y ^ { 10 } \sqrt [ 3 ] { 15 y ^ { 2 } }$ 
D)  $x ^ { 4 } y ^ { 5 } \sqrt [ 3 ] { 5 y }$ 
A)  $x ^ { 8 } y ^ { 10 } \sqrt [ 3 ] { 25 y ^ { 2 } }$ 
B)  $x ^ { 8 } y ^ { 10 } \sqrt [ 3 ] { 5 y ^ { 2 } }$ 
C)  $x ^ { 8 } y ^ { 10 } \sqrt [ 3 ] { 15 y ^ { 2 } }$ 
D)  $x ^ { 4 } y ^ { 5 } \sqrt [ 3 ] { 5 y }$

Question 17

Solve and check your solution(s). If the equation has no real solution, so state.
-$\sqrt [ 3 ] { 3 + 7 x } - \sqrt [ 3 ] { 4 - 2 x } = 0$

Accepted Answer

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

Question 18

Solve and check your solution(s). If the equation has no real solution, so state.
-$\sqrt { 2 x } + 4 = x + 0$

Accepted Answer

A) 8 
B) 2, 8 
C)  $- 4 , \frac { 4 } { 3 }$ 
D) -4 
A) 8 
B) 2, 8 
C)  $- 4 , \frac { 4 } { 3 }$ 
D) -4

Question 19

Simplify.
-$\text { If } f ( x ) = 2 \sqrt { 3 x } \text {, and } g ( x ) = \sqrt { 11 } + \sqrt { 3 x } \text {, find } ( f \cdot g ) ( x ) \text {. }$

Accepted Answer

A)  $6 \sqrt { 11 x } + 6 x$ 
B)  $2 \sqrt { 33 } + 3 x$ 
C)  $2 \sqrt { 11 } + 3 x$ 
D)  $2 \sqrt { 33 x } + 6 x$ 
A)  $6 \sqrt { 11 x } + 6 x$ 
B)  $2 \sqrt { 33 } + 3 x$ 
C)  $2 \sqrt { 11 } + 3 x$ 
D)  $2 \sqrt { 33 x } + 6 x$

Question 20

Solve and check your solution(s). If the equation has no real solution, so state.
-$\sqrt { x ^ { 2 } - 3 } = \sqrt { x + 3 }$

Accepted Answer

A) -2, 3 
B) -3, 3 
C) -3 
D) 2, 3 
A) -2, 3 
B) -3, 3 
C) -3 
D) 2, 3

Evaluate if possible. If the expression is not a real number, so state. - $32^{4 / 5}$

Simplify. - $3 \sqrt [ 3 ] { x ^ { 3 } y ^ { 13 } } + 2 x y \sqrt [ 3 ] { 27 y ^ { 10 } }$

Find the indicated value of the function. Use your calculator to approximate irrational numbers. Round irrational numbers to the nearest thousandth. - $\text { Find } f ( 0 ) \text { if } f ( x ) = \sqrt { x ^ { 2 } + 7 x }$

Evaluate if possible. If the expression is not a real number, so state. - $8 ^ { 4 / 3 }$

Simplify. - $\sqrt [ 3 ] { 16 } + \sqrt [ 3 ] { 128 }$

Simplify. Write the answer in exponential form without negative exponents. - $\left( x ^ { - 1 / 2 } \right) ^ { - 1 / 6 }$

Write as an absolute value. - $\sqrt { z ^ { 2 } - 12 z + 36 }$

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt [ 3 ] { 3 - 3 x } = 2$

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt { x + 9 } = \sqrt { x - 9 }$

Simplify. - $( \sqrt { 8 } + \sqrt { z } ) ( \sqrt { 8 } - \sqrt { z } )$

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt [ 4 ] { x + 7 } = \sqrt [ 4 ] { 5 x }$

Simplify. - $\sqrt { \frac { 100 } { 9 } }$

Multiply. Write the result in the form a + bi. - $( 2 + \sqrt { - 2 } ) ( 4 + \sqrt { - 2 } )$

Simplify. Write the answer in exponential form without negative exponents. - $\frac { x ^ { 3 } } { x ^ { - 1 / 5 } }$

Simplify. - $\left( \sqrt [ 3 ] { 5 x ^ { 12 } y ^ { 16 } } \right) ^ { 2 }$

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt [ 3 ] { 3 + 7 x } - \sqrt [ 3 ] { 4 - 2 x } = 0$

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt { 2 x } + 4 = x + 0$

Simplify. - $\text { If } f ( x ) = 2 \sqrt { 3 x } \text {, and } g ( x ) = \sqrt { 11 } + \sqrt { 3 x } \text {, find } ( f \cdot g ) ( x ) \text {. }$

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt { x ^ { 2 } - 3 } = \sqrt { x + 3 }$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Quadratic Functions

Exponential and Logarithmic Functions

Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Exam 7: Roots, Radicals, and Complex Numbers

Evaluate if possible. If the expression is not a real number, so state. - 324/532^{4 / 5}324/5

Simplify. - 3x3y133+2xy27y1033 \sqrt [ 3 ] { x ^ { 3 } y ^ { 13 } } + 2 x y \sqrt [ 3 ] { 27 y ^ { 10 } }33x3y13​+2xy327y10​

Find the indicated value of the function. Use your calculator to approximate irrational numbers. Round irrational numbers to the nearest thousandth. - Find f(0) if f(x)=x2+7x\text { Find } f ( 0 ) \text { if } f ( x ) = \sqrt { x ^ { 2 } + 7 x } Find f(0) if f(x)=x2+7x​

Evaluate if possible. If the expression is not a real number, so state. - 84/38 ^ { 4 / 3 }84/3

Simplify. - 163+1283\sqrt [ 3 ] { 16 } + \sqrt [ 3 ] { 128 }316​+3128​

Simplify. Write the answer in exponential form without negative exponents. - (x−1/2)−1/6\left( x ^ { - 1 / 2 } \right) ^ { - 1 / 6 }(x−1/2)−1/6

Write as an absolute value. - z2−12z+36\sqrt { z ^ { 2 } - 12 z + 36 }z2−12z+36​

Solve and check your solution(s). If the equation has no real solution, so state. - 3−3x3=2\sqrt [ 3 ] { 3 - 3 x } = 233−3x​=2

Solve and check your solution(s). If the equation has no real solution, so state. - x+9=x−9\sqrt { x + 9 } = \sqrt { x - 9 }x+9​=x−9​

Simplify. - (8+z)(8−z)( \sqrt { 8 } + \sqrt { z } ) ( \sqrt { 8 } - \sqrt { z } )(8​+z​)(8​−z​)

Solve and check your solution(s). If the equation has no real solution, so state. - x+74=5x4\sqrt [ 4 ] { x + 7 } = \sqrt [ 4 ] { 5 x }4x+7​=45x​

Simplify. - 1009\sqrt { \frac { 100 } { 9 } }9100​​

Multiply. Write the result in the form a + bi. - (2+−2)(4+−2)( 2 + \sqrt { - 2 } ) ( 4 + \sqrt { - 2 } )(2+−2​)(4+−2​)

Simplify. Write the answer in exponential form without negative exponents. - x3x−1/5\frac { x ^ { 3 } } { x ^ { - 1 / 5 } }x−1/5x3​

Simplify. - (5x12y163)2\left( \sqrt [ 3 ] { 5 x ^ { 12 } y ^ { 16 } } \right) ^ { 2 }(35x12y16​)2

Solve and check your solution(s). If the equation has no real solution, so state. - 3+7x3−4−2x3=0\sqrt [ 3 ] { 3 + 7 x } - \sqrt [ 3 ] { 4 - 2 x } = 033+7x​−34−2x​=0

Solve and check your solution(s). If the equation has no real solution, so state. - 2x+4=x+0\sqrt { 2 x } + 4 = x + 02x​+4=x+0

Simplify. - If f(x)=23x, and g(x)=11+3x, find (f⋅g)(x). \text { If } f ( x ) = 2 \sqrt { 3 x } \text {, and } g ( x ) = \sqrt { 11 } + \sqrt { 3 x } \text {, find } ( f \cdot g ) ( x ) \text {. } If f(x)=23x​, and g(x)=11​+3x​, find (f⋅g)(x).

Solve and check your solution(s). If the equation has no real solution, so state. - x2−3=x+3\sqrt { x ^ { 2 } - 3 } = \sqrt { x + 3 }x2−3​=x+3​