Question 1

Simplify by rationalizing the denominator.
-$\frac { y \sqrt { 2 } - 3 } { 2 \sqrt { 2 } + 3 }$

Accepted Answer

A)  $\frac { y } { 2 } - 1$ 
B)  $\frac { \mathrm { y } - 1 } { 3 }$ 
C)  $\frac { 4 y - 3 y \sqrt { 3 } - 3 } { - 1 }$ 
D)  $\frac { 4 y - 3 y \sqrt { 2 } - 6 \sqrt { 2 } + 9 } { - 1 }$ 
A)  $\frac { y } { 2 } - 1$ 
B)  $\frac { \mathrm { y } - 1 } { 3 }$ 
C)  $\frac { 4 y - 3 y \sqrt { 3 } - 3 } { - 1 }$ 
D)  $\frac { 4 y - 3 y \sqrt { 2 } - 6 \sqrt { 2 } + 9 } { - 1 }$

Question 2

Use absolute value to evaluate.
-$$\sqrt [ 4 ] { ( - 2 ) ^ { 4 } }$$

Accepted Answer

A) -2 
B) 16 
C) 2 
D) not a real number 
A) -2 
B) 16 
C) 2 
D) not a real number

Question 3

Simplify.
-$\sqrt [ 4 ] { \frac { x ^ { 20 } y ^ { 16 } } { y ^ { - 4 } } }$

Accepted Answer

A)  $x ^ { 5 } y ^ { 5 }$ 
B)  $x ^ { 80 } y ^ { 80 }$ 
C)  $x ^ { 20 } y ^ { 5 }$ 
D)  $x ^ { 5 } y ^ { 3 }$ 
A)  $x ^ { 5 } y ^ { 5 }$ 
B)  $x ^ { 80 } y ^ { 80 }$ 
C)  $x ^ { 20 } y ^ { 5 }$ 
D)  $x ^ { 5 } y ^ { 3 }$

Question 4

Write the expression in exponential form. Assume that all variables represent positive real numbers.
-$\sqrt [ 6 ] { x }$

Accepted Answer

A)  $x ^ { - 1 / 3 }$ 
B)  $x ^ { - 3 }$ 
C)  $x ^ { 3 }$ 
D)  $\mathrm { x } ^ { 1 / 3 }$ 
A)  $x ^ { - 1 / 3 }$ 
B)  $x ^ { - 3 }$ 
C)  $x ^ { 3 }$ 
D)  $\mathrm { x } ^ { 1 / 3 }$

Question 5

Simplify. Assume all variables represent positive real numbers.
-$\frac { 64 \sqrt { 13 } } { 40 \sqrt { 5 } }$

Accepted Answer

A)  $\frac { 8 \sqrt { 65 } } { 5 }$ 
B)  $\frac { 8 \sqrt { 65 } } { 25 }$ 
C)  $\frac { 8 \sqrt { 13 } } { 25 }$ 
D)  $\frac { 8 \sqrt { 13 } } { 5 }$ 
A)  $\frac { 8 \sqrt { 65 } } { 5 }$ 
B)  $\frac { 8 \sqrt { 65 } } { 25 }$ 
C)  $\frac { 8 \sqrt { 13 } } { 25 }$ 
D)  $\frac { 8 \sqrt { 13 } } { 5 }$

Question 6

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

Accepted Answer

A) 64 
B) -16 
C) 16 
D) not a real number 
A) 64 
B) -16 
C) 16 
D) not a real number

Question 7

Evaluate if possible. If the expression is not a real number, so state.
-$16 ^ { 5 / 4 }$

Accepted Answer

A) 128 
B) 512 
C) 256 
D) 32 
A) 128 
B) 512 
C) 256 
D) 32

Question 8

Write the expression as a complex number in the form a + bi.
-2i

Accepted Answer

A) 2 + 0i 
B) 2 - 2i 
C) 2 + 2i 
D) 0 + 2i 
A) 2 + 0i 
B) 2 - 2i 
C) 2 + 2i 
D) 0 + 2i

Question 9

Add or subtract.
-$5 i + ( - 2 - i )$

Accepted Answer

A) 2 - 6i 
B) -2 + 6i 
C) 2 - 4i 
D) -2 + 4i 
A) 2 - 6i 
B) -2 + 6i 
C) 2 - 4i 
D) -2 + 4i

Question 10

Simplify.
-$6 \sqrt { 7 } + 9 \sqrt { 7 } - 12$

Accepted Answer

A)  $- 3 \sqrt { 7 } - 12$ 
B)  $27 \sqrt { 7 }$ 
C)  $3 \sqrt { 7 }$ 
D)  $15 \sqrt { 7 } - 12$ 
A)  $- 3 \sqrt { 7 } - 12$ 
B)  $27 \sqrt { 7 }$ 
C)  $3 \sqrt { 7 }$ 
D)  $15 \sqrt { 7 } - 12$

Question 11

Solve and check your solution(s). If the equation has no real solution, so state.
-$\sqrt { 3 x + 18 } = x$

Accepted Answer

A) 6 
B) - 9 
C) -3, 6 
D) no real solution 
A) 6 
B) - 9 
C) -3, 6 
D) no real solution

Question 12

Simplify.
-6a + 5 96a + 4 150a

Accepted Answer

A) 9 6a 
B) 9 252a 
C) 41 252a 
D) 41 6a 
A) 9 6a 
B) 9 252a 
C) 41 252a 
D) 41 6a

Question 13

Simplify by rationalizing the denominator.
-$\frac { \sqrt { 405 x } } { x + \sqrt { y } }$

Accepted Answer

A)  $\frac { 9 x \sqrt { 5 x } - 9 \sqrt { 5 x y } } { x - y }$ 
B)  $\frac { 9 x \sqrt { 5 x } - 9 \sqrt { 5 x y } } { x ^ { 2 } - y }$ 
C)  $\frac { 9 x \sqrt { 5 x } + 9 \sqrt { 5 x y } } { x ^ { 2 } - y ^ { 2 } }$ 
D)  $\frac { 9 x \sqrt { 5 x } - 9 \sqrt { 5 x y } } { x ^ { 2 } - y ^ { 2 } }$ 
A)  $\frac { 9 x \sqrt { 5 x } - 9 \sqrt { 5 x y } } { x - y }$ 
B)  $\frac { 9 x \sqrt { 5 x } - 9 \sqrt { 5 x y } } { x ^ { 2 } - y }$ 
C)  $\frac { 9 x \sqrt { 5 x } + 9 \sqrt { 5 x y } } { x ^ { 2 } - y ^ { 2 } }$ 
D)  $\frac { 9 x \sqrt { 5 x } - 9 \sqrt { 5 x y } } { x ^ { 2 } - y ^ { 2 } }$

Question 14

Solve and check your solution(s). If the equation has no real solution, so state.
-$$\sqrt { x ^ { 2 } - 3 x + 71 } = x + 4$$

Accepted Answer

A) 9 
B) -5 
C) 1 
D) 5 
A) 9 
B) -5 
C) 1 
D) 5

Question 15

Multiply. Write the result in the form a + bi.
-( $( 3 - 7 i ) ( 3 - 3 i )$

Accepted Answer

A)  $30 - 12 \mathrm { i }$ 
B)  $- 12 - 30 \mathrm { i }$ 
C)  $21 i ^ { 2 } - 30 i + 9$ 
D)  $- 12 + 30 \mathrm { i }$ 
A)  $30 - 12 \mathrm { i }$ 
B)  $- 12 - 30 \mathrm { i }$ 
C)  $21 i ^ { 2 } - 30 i + 9$ 
D)  $- 12 + 30 \mathrm { i }$

Question 16

Simplify.
-$\sqrt [ 4 ] { x ^ { 23 } }$

Accepted Answer

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

Question 17

Write the word or phrase that best completes each statement or answers the question.
-Solve the formula a r $$r = \sqrt { \frac { 2 A } { \theta } } \text { for } \theta$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 18

Multiply.
-$- 2 x ^ { - 3 / 3 } \left( 5 x ^ { 1 / 3 } - x ^ { 3 } \right)$

Accepted Answer

A)  $- \frac { 10 } { x ^ { 4 / 3 } } - 2 x ^ { 6 / 3 }$ 
B)  $- \frac { 10 } { x ^ { 2 / 3 } } + 2 x ^ { 6 / 3 }$ 
C)  $- \frac { 10 } { x ^ { 4 / 3 } } + 2 x ^ { 6 / 3 }$ 
D)  $- \frac { 10 } { x ^ { 2 / 3 } } - 2 x ^ { 6 / 3 }$ 
A)  $- \frac { 10 } { x ^ { 4 / 3 } } - 2 x ^ { 6 / 3 }$ 
B)  $- \frac { 10 } { x ^ { 2 / 3 } } + 2 x ^ { 6 / 3 }$ 
C)  $- \frac { 10 } { x ^ { 4 / 3 } } + 2 x ^ { 6 / 3 }$ 
D)  $- \frac { 10 } { x ^ { 2 / 3 } } - 2 x ^ { 6 / 3 }$

Question 19

Simplify by rationalizing the denominator.
-$\frac { \sqrt { x } - 3 } { \sqrt { x } + 3 }$

Accepted Answer

A)  $- 6 \sqrt { x }$ 
B)  $\frac { x - 6 \sqrt { x } + 9 } { x - 9 }$ 
C)  $- 1$ 
D)  $\frac { x + 9 } { x - 9 }$ 
A)  $- 6 \sqrt { x }$ 
B)  $\frac { x - 6 \sqrt { x } + 9 } { x - 9 }$ 
C)  $- 1$ 
D)  $\frac { x + 9 } { x - 9 }$

Question 20

Add or subtract.
-$( \sqrt { 80 } - \sqrt { - 80 } ) + ( 4 \sqrt { 5 } + \sqrt { - 320 } )$

Accepted Answer

A)  $8 \sqrt { 5 } + 4 \sqrt { 5 }$ 
B)  $8 \sqrt { 5 } - 4 \mathrm { i } \sqrt { 5 }$ 
C)  $8 \sqrt { 5 } + 4 i \sqrt { 5 }$ 
D)  $8 \sqrt { 5 } + 12 i \sqrt { 5 }$ 
A)  $8 \sqrt { 5 } + 4 \sqrt { 5 }$ 
B)  $8 \sqrt { 5 } - 4 \mathrm { i } \sqrt { 5 }$ 
C)  $8 \sqrt { 5 } + 4 i \sqrt { 5 }$ 
D)  $8 \sqrt { 5 } + 12 i \sqrt { 5 }$

Simplify by rationalizing the denominator. - $\frac { y \sqrt { 2 } - 3 } { 2 \sqrt { 2 } + 3 }$

Use absolute value to evaluate. - $\sqrt [ 4 ] { ( - 2 ) ^ { 4 } }$

Simplify. - $\sqrt [ 4 ] { \frac { x ^ { 20 } y ^ { 16 } } { y ^ { - 4 } } }$

Write the expression in exponential form. Assume that all variables represent positive real numbers. - $\sqrt [ 6 ] { x }$

Simplify. Assume all variables represent positive real numbers. - $\frac { 64 \sqrt { 13 } } { 40 \sqrt { 5 } }$

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

Evaluate if possible. If the expression is not a real number, so state. - $16 ^ { 5 / 4 }$

Write the expression as a complex number in the form a + bi. -2i

Add or subtract. - $5 i + ( - 2 - i )$

Simplify. - $6 \sqrt { 7 } + 9 \sqrt { 7 } - 12$

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt { 3 x + 18 } = x$

Simplify. -6a + 5 96a + 4 150a

Simplify by rationalizing the denominator. - $\frac { \sqrt { 405 x } } { x + \sqrt { y } }$

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt { x ^ { 2 } - 3 x + 71 } = x + 4$

Multiply. Write the result in the form a + bi. -( $( 3 - 7 i ) ( 3 - 3 i )$

Simplify. - $\sqrt [ 4 ] { x ^ { 23 } }$

Write the word or phrase that best completes each statement or answers the question. -Solve the formula a r $r = \sqrt { \frac { 2 A } { \theta } } \text { for } \theta$

Multiply. - $- 2 x ^ { - 3 / 3 } \left( 5 x ^ { 1 / 3 } - x ^ { 3 } \right)$

Simplify by rationalizing the denominator. - $\frac { \sqrt { x } - 3 } { \sqrt { x } + 3 }$

Add or subtract. - $( \sqrt { 80 } - \sqrt { - 80 } ) + ( 4 \sqrt { 5 } + \sqrt { - 320 } )$

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

Simplify by rationalizing the denominator. - y2−322+3\frac { y \sqrt { 2 } - 3 } { 2 \sqrt { 2 } + 3 }22​+3y2​−3​

Use absolute value to evaluate. - (−2)44\sqrt [ 4 ] { ( - 2 ) ^ { 4 } }4(−2)4​

Simplify. - x20y16y−44\sqrt [ 4 ] { \frac { x ^ { 20 } y ^ { 16 } } { y ^ { - 4 } } }4y−4x20y16​​

Write the expression in exponential form. Assume that all variables represent positive real numbers. - x6\sqrt [ 6 ] { x }6x​

Simplify. Assume all variables represent positive real numbers. - 6413405\frac { 64 \sqrt { 13 } } { 40 \sqrt { 5 } }405​6413​​

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

Evaluate if possible. If the expression is not a real number, so state. - 165/416 ^ { 5 / 4 }165/4