Question 1

Write as an absolute value.
-$\sqrt { ( x + 2 ) ^ { 2 } }$

Accepted Answer

A) x + 2 
B)  $| x + 2 |$ 
C)  $x ^ { 2 } + 4 x + 4$ 
D)  $\left| x ^ { 2 } + 4 x + 4 \right|$ 
A) x + 2 
B)  $| x + 2 |$ 
C)  $x ^ { 2 } + 4 x + 4$ 
D)  $\left| x ^ { 2 } + 4 x + 4 \right|$

Question 2

Simplify.
-$\sqrt { \frac { 100 z ^ { 24 } } { 121 } }$

Accepted Answer

A)  $\frac { 10 z ^ { 12 } } { 121 }$ 
B)  $\frac { 100 z ^ { 12 } } { 121 }$ 
C)  $\frac { 10 z^{12} } { 11 }$ 
D)  $\frac { 10 z ^ { 22 } } { 11 }$ 
A)  $\frac { 10 z ^ { 12 } } { 121 }$ 
B)  $\frac { 100 z ^ { 12 } } { 121 }$ 
C)  $\frac { 10 z^{12} } { 11 }$ 
D)  $\frac { 10 z ^ { 22 } } { 11 }$

Question 3

Simplify.
-$\sqrt [ 3 ] { 729 x ^ { 4 } y ^ { 5 } }$

Accepted Answer

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

Question 4

Multiply. Write the result in the form a + bi.
-4 $4 i ( 2 - 6 i )$

Accepted Answer

A)  $8 \mathrm { i } - 24 \mathrm { i } ^ { 2 }$ 
B)  $8 \mathrm { i } - 24$ 
C)  $24 + 8 \mathrm { i }$ 
D)  $8 \mathrm { i } + 24 \mathrm { i } ^ { 2 }$ 
A)  $8 \mathrm { i } - 24 \mathrm { i } ^ { 2 }$ 
B)  $8 \mathrm { i } - 24$ 
C)  $24 + 8 \mathrm { i }$ 
D)  $8 \mathrm { i } + 24 \mathrm { i } ^ { 2 }$

Question 5

Write the word or phrase that best completes each statement or answers the question.
-$\frac { \sqrt [ 3 ] { x + 7 } } { \sqrt [ 4 ] { ( x + 7 ) ^ { 7 } } }$

Accepted Answer

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

Question 6

Solve the problem.
-A right circular cone used for packaging candy needs to hold 2 cubic inches of candy and be 3 inches tall. Let $r = \sqrt { \frac { 3 V } { \pi h } }$ repr represent the radius of the circular base where V represents the volume of the cone and h represents the height of the cone. Approximate the radius of this package.

Accepted Answer

A) r = 1.41 in. 
B) r = 1.38 in. 
C) r = 0.56 in. 
D) r = 0.80 in. 
A) r = 1.41 in. 
B) r = 1.38 in. 
C) r = 0.56 in. 
D) r = 0.80 in.

Question 7

Simplify.
-$\sqrt { 5 x ^ { 2 } } \sqrt { 15 x }$

Accepted Answer

A)  $5 x \sqrt { 3 x ^ { 2 } }$ 
B)  $5 x ^ { 2 } \sqrt { 3 x }$ 
C)  $5 x \sqrt { 3 }$ 
D)  $5 x \sqrt { 3 x }$ 
A)  $5 x \sqrt { 3 x ^ { 2 } }$ 
B)  $5 x ^ { 2 } \sqrt { 3 x }$ 
C)  $5 x \sqrt { 3 }$ 
D)  $5 x \sqrt { 3 x }$

Question 8

Add or subtract.
-$( 3 - 3 i ) + ( 2 - 7 i ) + ( 4 + 5 i )$

Accepted Answer

A) 5 - 10i 
B)  $1 - 15 i$ 
C)  $5 + 9 i$ 
D)  $9 - 5 i$ 
A) 5 - 10i 
B)  $1 - 15 i$ 
C)  $5 + 9 i$ 
D)  $9 - 5 i$

Question 9

Simplify.
-27 + 147

Accepted Answer

A) -4 6 
B) -4 3 
C) -12 
D) 10 3 
A) -4 6 
B) -4 3 
C) -12 
D) 10 3

Question 10

Simplify.
-$\sqrt { 175 } \sqrt { 7 }$

Accepted Answer

A) 1225 
B)  $5 \sqrt { 7 }$ 
C) 35 
D)  $7 \sqrt { 5 }$ 
A) 1225 
B)  $5 \sqrt { 7 }$ 
C) 35 
D)  $7 \sqrt { 5 }$

Question 11

Simplify by rationalizing the denominator.
-$\frac { \sqrt { 6 } } { \sqrt { 17 } + 2 }$

Accepted Answer

A)  $\frac { \sqrt { 102 } + 2 \sqrt { 6 } } { 13 }$ 
B)  $\frac { 3 \sqrt { 102 } + 17 \sqrt { 34 } } { 6 }$ 
C)  $\frac { \sqrt { 102 } - 2 \sqrt { 6 } } { 19 }$ 
D)  $\frac { \sqrt { 102 } - 2 \sqrt { 6 } } { 13 }$ 
A)  $\frac { \sqrt { 102 } + 2 \sqrt { 6 } } { 13 }$ 
B)  $\frac { 3 \sqrt { 102 } + 17 \sqrt { 34 } } { 6 }$ 
C)  $\frac { \sqrt { 102 } - 2 \sqrt { 6 } } { 19 }$ 
D)  $\frac { \sqrt { 102 } - 2 \sqrt { 6 } } { 13 }$

Question 12

Simplify.
-$\sqrt { 20 }$

Accepted Answer

A)  $4 \sqrt { 5 }$ 
B) 10 
C)  $\sqrt { 20 }$ 
D)  $2 \sqrt { 5 }$ 
A)  $4 \sqrt { 5 }$ 
B) 10 
C)  $\sqrt { 20 }$ 
D)  $2 \sqrt { 5 }$

Question 13

Solve and check your solution(s). If the equation has no real solution, so state.
-$\sqrt { 2 y + 5 } + \sqrt { 2 y + 8 } = \sqrt { 8 y + 25 }$

Accepted Answer

A) 0 
B) 1 
C) -2 
D) no real solution 
A) 0 
B) 1 
C) -2 
D) no real solution

Question 14

Evaluate if possible. If the expression is not a real number, so state.
-$\left( \frac { 16 } { 81 } \right) ^ { 1 / 4 }$

Accepted Answer

A) 24 
B)  $\frac { 2 } { 3 }$ 
C)  $\frac { 3 } { 2 }$ 
D) 6 
A) 24 
B)  $\frac { 2 } { 3 }$ 
C)  $\frac { 3 } { 2 }$ 
D) 6

Question 15

Factor. Write the answer without negative exponents.
-$x ^ { - 1 / 3 } + x ^ { 1 / 3 }$

Accepted Answer

A)  $x ^ { 1 / 3 } \left( 1 + x ^ { 2 / 3 } \right)$ 
B) 1 
C)  $\frac { 1 + x ^ { 2 / 3 } } { x ^ { 1 / 3 } }$ 
D) 0 
A)  $x ^ { 1 / 3 } \left( 1 + x ^ { 2 / 3 } \right)$ 
B) 1 
C)  $\frac { 1 + x ^ { 2 / 3 } } { x ^ { 1 / 3 } }$ 
D) 0

Question 16

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

Accepted Answer

A)  $\frac { 1 } { x ^ { 15 / 28 } }$ 
B)  $\frac { 1 } { x ^ { 28 / 15 } }$ 
C)  $x ^ { 1 / 3 }$ 
D)  $\frac { 1 } { x ^ { 1 / 3 } }$ 
A)  $\frac { 1 } { x ^ { 15 / 28 } }$ 
B)  $\frac { 1 } { x ^ { 28 / 15 } }$ 
C)  $x ^ { 1 / 3 }$ 
D)  $\frac { 1 } { x ^ { 1 / 3 } }$

Question 17

Simplify.
-$\sqrt { \frac { x ^ { 8 } } { 121 } }$

Accepted Answer

A)  $\frac { x ^ { 4 } } { 11 }$ 
B)  $\frac { x ^ { 6 } } { 11 }$ 
C)  $\frac { x ^ { 4 } } { 121 }$ 
D)  $\frac { x ^ { 8 } } { 11 }$ 
A)  $\frac { x ^ { 4 } } { 11 }$ 
B)  $\frac { x ^ { 6 } } { 11 }$ 
C)  $\frac { x ^ { 4 } } { 121 }$ 
D)  $\frac { x ^ { 8 } } { 11 }$

Question 18

Simplify.
-$\sqrt { 72 } \sqrt { 50 }$

Accepted Answer

A)  $30 \sqrt { 2 }$ 
B) 30 
C) 50 
D) 60 
A)  $30 \sqrt { 2 }$ 
B) 30 
C) 50 
D) 60

Write as an absolute value. - $\sqrt { ( x + 2 ) ^ { 2 } }$

Simplify. - $\sqrt { \frac { 100 z ^ { 24 } } { 121 } }$

Simplify. - $\sqrt [ 3 ] { 729 x ^ { 4 } y ^ { 5 } }$

Multiply. Write the result in the form a + bi. -4 $4 i ( 2 - 6 i )$

Write the word or phrase that best completes each statement or answers the question. - $\frac { \sqrt [ 3 ] { x + 7 } } { \sqrt [ 4 ] { ( x + 7 ) ^ { 7 } } }$

Simplify. - $\sqrt { 5 x ^ { 2 } } \sqrt { 15 x }$

Add or subtract. - $( 3 - 3 i ) + ( 2 - 7 i ) + ( 4 + 5 i )$

Simplify. -27 + 147

Simplify. - $\sqrt { 175 } \sqrt { 7 }$

Simplify by rationalizing the denominator. - $\frac { \sqrt { 6 } } { \sqrt { 17 } + 2 }$

Simplify. - $\sqrt { 20 }$

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt { 2 y + 5 } + \sqrt { 2 y + 8 } = \sqrt { 8 y + 25 }$

Evaluate if possible. If the expression is not a real number, so state. - $\left( \frac { 16 } { 81 } \right) ^ { 1 / 4 }$

Factor. Write the answer without negative exponents. - $x ^ { - 1 / 3 } + x ^ { 1 / 3 }$

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

Simplify. - $\sqrt { \frac { x ^ { 8 } } { 121 } }$

Simplify. - $\sqrt { 72 } \sqrt { 50 }$

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

Write as an absolute value. - (x+2)2\sqrt { ( x + 2 ) ^ { 2 } }(x+2)2​

Simplify. - 100z24121\sqrt { \frac { 100 z ^ { 24 } } { 121 } }121100z24​​

Simplify. - 729x4y53\sqrt [ 3 ] { 729 x ^ { 4 } y ^ { 5 } }3729x4y5​

Multiply. Write the result in the form a + bi. -4 4i(2−6i)4 i ( 2 - 6 i )4i(2−6i)

Write the word or phrase that best completes each statement or answers the question. - x+73(x+7)74\frac { \sqrt [ 3 ] { x + 7 } } { \sqrt [ 4 ] { ( x + 7 ) ^ { 7 } } }4(x+7)7​3x+7​​

Simplify. - 5x215x\sqrt { 5 x ^ { 2 } } \sqrt { 15 x }5x2​15x​

Add or subtract. - (3−3i)+(2−7i)+(4+5i)( 3 - 3 i ) + ( 2 - 7 i ) + ( 4 + 5 i )(3−3i)+(2−7i)+(4+5i)