Question 1

Write as an absolute value.
-$$\sqrt { ( 11 x - 3 y ) ^ { 2 } }$$

Accepted Answer

A)  $11 x + 3 y$ 
B)  $11 x - 3 y$ 
C)  $| 11 x - 3 y |$ 
D)  $| 11 x + 3 y |$ 
A)  $11 x + 3 y$ 
B)  $11 x - 3 y$ 
C)  $| 11 x - 3 y |$ 
D)  $| 11 x + 3 y |$

Question 2

Add or subtract.
-(9 + 3i)- (-7 + i)

Accepted Answer

A) 16 + 2i 
B) -16 - 2i 
C) 2 + 4i 
D) 16 - 2i 
A) 16 + 2i 
B) -16 - 2i 
C) 2 + 4i 
D) 16 - 2i

Question 3

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

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 3 } { 2 }$ 
C)  $\frac { 5 } { 2 }$ 
D) no real solution 
A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 3 } { 2 }$ 
C)  $\frac { 5 } { 2 }$ 
D) no real solution

Question 4

Divide.
-$\frac { 5 } { 1 - 3 i }$

Accepted Answer

A)  $\frac { 1 } { 2 } + \frac { 3 } { 2 } \mathrm { i }$ 
B)  $\frac { 1 } { 2 } - \frac { 3 } { 2 } \mathrm { i }$ 
C)  $- \frac { 5 } { 8 } - \frac { 15 } { 8 } i$ 
D)  $- \frac { 5 } { 8 } + \frac { 15 } { 8 } \mathrm { i }$ 
A)  $\frac { 1 } { 2 } + \frac { 3 } { 2 } \mathrm { i }$ 
B)  $\frac { 1 } { 2 } - \frac { 3 } { 2 } \mathrm { i }$ 
C)  $- \frac { 5 } { 8 } - \frac { 15 } { 8 } i$ 
D)  $- \frac { 5 } { 8 } + \frac { 15 } { 8 } \mathrm { i }$

Question 5

Add or subtract.
-7i + (-2 - i)

Accepted Answer

A) 2 - 6i 
B) -2 + 6i 
C) 2 - 8i 
D) -2 + 8i 
A) 2 - 6i 
B) -2 + 6i 
C) 2 - 8i 
D) -2 + 8i

Question 6

Use absolute value to evaluate.
-$\sqrt { ( - 2.43 ) ^ { 2 } }$

Accepted Answer

A) -2.43 
B) 5.9 
C) 2.43 
D) not a real number 
A) -2.43 
B) 5.9 
C) 2.43 
D) not a real number

Question 7

Simplify the radical expression. Write the answer in radical form when appropriate.
-$\sqrt [ 3 ] { x ^ { 15 } }$

Accepted Answer

A)  $x ^ { 3 }$ 
B)  $x ^ { 12 }$ 
C)  $x ^ { 5 }$ 
D)  $x ^ { - 5 }$ 
A)  $x ^ { 3 }$ 
B)  $x ^ { 12 }$ 
C)  $x ^ { 5 }$ 
D)  $x ^ { - 5 }$

Question 8

Simplify by rationalizing the denominator.
-$\frac { 9 \sqrt { 3 } } { \sqrt { x } - 4 }$

Accepted Answer

A)  $\frac { 9 \sqrt { 3 x } + 36 \sqrt { 3 } } { x - 4 }$ 
B)  $\frac { 9 \sqrt { 3 x } - 36 \sqrt { 3 } } { x + 16 }$ 
C)  $\frac { 9 \sqrt { 3 x } + 36 \sqrt { 3 } } { x - 16 }$ 
D)  $\frac { 9 \sqrt { 3 x } - 36 \sqrt { 3 } } { x - 4 }$ 
A)  $\frac { 9 \sqrt { 3 x } + 36 \sqrt { 3 } } { x - 4 }$ 
B)  $\frac { 9 \sqrt { 3 x } - 36 \sqrt { 3 } } { x + 16 }$ 
C)  $\frac { 9 \sqrt { 3 x } + 36 \sqrt { 3 } } { x - 16 }$ 
D)  $\frac { 9 \sqrt { 3 x } - 36 \sqrt { 3 } } { x - 4 }$

Question 9

Write as an absolute value.
-$$\sqrt { \mathrm { d } ^ { 2 } }$$

Accepted Answer

A)  $| \mathrm { d } |$ 
B) d 
C)  $\mathrm { d } ^ { 2 }$ 
D) -d 
A)  $| \mathrm { d } |$ 
B) d 
C)  $\mathrm { d } ^ { 2 }$ 
D) -d

Question 10

Write the expression as a complex number in the form a + bi.
-$\sqrt { - 144 }$

Accepted Answer

A) 0 - 12i 
B) -12 + 0i 
C) 0 + 12i 
D) 12 + 0i 
A) 0 - 12i 
B) -12 + 0i 
C) 0 + 12i 
D) 12 + 0i

Question 11

Evaluate if possible. If the expression is not a real number, so state.
-$( - 16 ) ^ { 1 / 2 }$

Accepted Answer

A) 4 
B) -4 
C) 256 
D) not a real number 
A) 4 
B) -4 
C) 256 
D) not a real number

Question 12

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.
-$$\sqrt [ 4 ] { - 81 }$$

Accepted Answer

A) -3 
B) -36 
C) -12 
D) not a real number 
A) -3 
B) -36 
C) -12 
D) not a real number

Question 13

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

Accepted Answer

A)  $\frac { 5 \sqrt { 13 z } } { 13 }$ 
B)  $\frac { \sqrt { 65 } } { 13 }$ 
C)  $\frac { 5 \sqrt { 13 z } } { 169 z }$ 
D)  $5 \sqrt { z }$ 
A)  $\frac { 5 \sqrt { 13 z } } { 13 }$ 
B)  $\frac { \sqrt { 65 } } { 13 }$ 
C)  $\frac { 5 \sqrt { 13 z } } { 169 z }$ 
D)  $5 \sqrt { z }$

Question 14

Evaluate if possible. If the expression is not a real number, so state.
-$\left( \frac { 27 } { 64 } \right) ^ { - 1 / 3 }$

Accepted Answer

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

Question 15

Solve the problem.
-Use the Pythagorean Theorem to find the length of the unknown side of the triangle. Write the answer as a radical in simplified form.

Accepted Answer

A)  $25 \sqrt { 7 }$ 
B)  $10 \sqrt { 7 }$ 
C)  $5 \sqrt { 7 }$ 
D) 35 
A)  $25 \sqrt { 7 }$ 
B)  $10 \sqrt { 7 }$ 
C)  $5 \sqrt { 7 }$ 
D) 35

Question 16

Write the word or phrase that best completes each statement or answers the question.
-Solve the formulaa r $$\mathrm { r } = \sqrt { \frac { 3 \mathrm {~V} } { \pi \mathrm { h } } } \text { for } \mathrm { V }$$

Accepted Answer

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

Question 17

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.
-$$- \sqrt [ 3 ] { - 343 }$$

Accepted Answer

A) 7 
B) -7 
C) -18.52 
D) not a real number 
A) 7 
B) -7 
C) -18.52 
D) not a real number

Question 18

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.
-$$\sqrt [ 4 ] { 16 }$$

Accepted Answer

A) 8 
B) 2 
C) 16 
D) not a real number 
A) 8 
B) 2 
C) 16 
D) not a real number

Question 19

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest
hundredth. If the expression is not a real number, so state.
-$\sqrt { 25 }$

Accepted Answer

A) 625 
B) 5 
C)  $\frac { 1 } { 25 }$ 
D) not a real number 
A) 625 
B) 5 
C)  $\frac { 1 } { 25 }$ 
D) not a real number

Question 20

Evaluate if possible. If the expression is not a real number, so state.
-$$\left( \frac { 1 } { 243 } \right) ^ { - 1 / 5 }$$

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B) 3 
C) -3 
D)  $\frac { - 1 } { 3 }$ 
A)  $\frac { 1 } { 3 }$ 
B) 3 
C) -3 
D)  $\frac { - 1 } { 3 }$

Write as an absolute value. - $\sqrt { ( 11 x - 3 y ) ^ { 2 } }$

Add or subtract. -(9 + 3i)- (-7 + i)

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

Divide. - $\frac { 5 } { 1 - 3 i }$

Add or subtract. -7i + (-2 - i)

Use absolute value to evaluate. - $\sqrt { ( - 2.43 ) ^ { 2 } }$

Simplify the radical expression. Write the answer in radical form when appropriate. - $\sqrt [ 3 ] { x ^ { 15 } }$

Simplify by rationalizing the denominator. - $\frac { 9 \sqrt { 3 } } { \sqrt { x } - 4 }$

Write as an absolute value. - $\sqrt { \mathrm { d } ^ { 2 } }$

Write the expression as a complex number in the form a + bi. - $\sqrt { - 144 }$

Evaluate if possible. If the expression is not a real number, so state. - $( - 16 ) ^ { 1 / 2 }$

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest hundredth. If the expression is not a real number, so state. - $\sqrt [ 4 ] { - 81 }$

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

Evaluate if possible. If the expression is not a real number, so state. - $\left( \frac { 27 } { 64 } \right) ^ { - 1 / 3 }$

Solve the problem. -Use the Pythagorean Theorem to find the length of the unknown side of the triangle. Write the answer as a radical in simplified form.

Write the word or phrase that best completes each statement or answers the question. -Solve the formulaa r $\mathrm { r } = \sqrt { \frac { 3 \mathrm {~V} } { \pi \mathrm { h } } } \text { for } \mathrm { V }$

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest hundredth. If the expression is not a real number, so state. - $- \sqrt [ 3 ] { - 343 }$

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest hundredth. If the expression is not a real number, so state. - $\sqrt [ 4 ] { 16 }$

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest hundredth. If the expression is not a real number, so state. - $\sqrt { 25 }$

Evaluate if possible. If the expression is not a real number, so state. - $\left( \frac { 1 } { 243 } \right) ^ { - 1 / 5 }$

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. - (11x−3y)2\sqrt { ( 11 x - 3 y ) ^ { 2 } }(11x−3y)2​

Add or subtract. -(9 + 3i)- (-7 + i)

Solve and check your solution(s). If the equation has no real solution, so state. - 4x−23=2\sqrt [ 3 ] { 4 x - 2 } = 234x−2​=2

Divide. - 51−3i\frac { 5 } { 1 - 3 i }1−3i5​

Add or subtract. -7i + (-2 - i)

Use absolute value to evaluate. - (−2.43)2\sqrt { ( - 2.43 ) ^ { 2 } }(−2.43)2​

Simplify the radical expression. Write the answer in radical form when appropriate. - x153\sqrt [ 3 ] { x ^ { 15 } }3x15​

Simplify by rationalizing the denominator. - 93x−4\frac { 9 \sqrt { 3 } } { \sqrt { x } - 4 }x​−493​​

Write as an absolute value. - d2\sqrt { \mathrm { d } ^ { 2 } }d2​

Write the expression as a complex number in the form a + bi. - −144\sqrt { - 144 }−144​

Evaluate if possible. If the expression is not a real number, so state. - (−16)1/2( - 16 ) ^ { 1 / 2 }(−16)1/2

Evaluate the radical expression if it is a real number. Use a calculator to approximate irrational numbers to the nearest hundredth. If the expression is not a real number, so state. - −814\sqrt [ 4 ] { - 81 }4−81​

Simplify. Assume all variables represent positive real numbers. - 5z13z\frac { 5 z } { \sqrt { 13 z } }13z​5z​

Evaluate if possible. If the expression is not a real number, so state. - (2764)−1/3\left( \frac { 27 } { 64 } \right) ^ { - 1 / 3 }(6427​)−1/3