Question 1

Solve the equation. $$- 4 + \sqrt { 3 x + 5 } = 3$$

Accepted Answer

$$\left\{ \frac { 44 } { 3 } \right\}$$

Question 2

The annual rate of return on an initial investment of P dollars is given by $r = \left( \frac { A } { P } \right) ^ { 1 / t } - 1$ where A is the current value and t is the number of years since the money was invested. Find the annual rate of return on a $22,000 investment that grew to $32,000 after 10 years. Round to the
Nearest hundredth of a percent.

Accepted Answer

A)  13.82% 
B)  23.82% 
C)  0.04% 
D)  3.82% 
A)  13.82% 
B)  23.82% 
C)  0.04% 
D)  3.82% D

Question 3

Simplify the radical. $\sqrt [ 4 ] { q ^ { 13 } }$

Accepted Answer

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

Question 4

Rationalize the denominator and simplify completely. $\sqrt { \frac { x ^ { 3 } } { 19 } }$

Accepted Answer

A)  $\frac { \sqrt { x ^ { 3 } } } { \sqrt { 19 } }$ 
B)  $\frac { \sqrt { 19 x ^ { 3 } } } { 19 }$ 
C)  $\frac { x \sqrt { 19 x } } { 19 }$ 
D)  $\frac { x \sqrt { x } } { \sqrt { 19 } }$ 
A)  $\frac { \sqrt { x ^ { 3 } } } { \sqrt { 19 } }$ 
B)  $\frac { \sqrt { 19 x ^ { 3 } } } { 19 }$ 
C)  $\frac { x \sqrt { 19 x } } { 19 }$ 
D)  $\frac { x \sqrt { x } } { \sqrt { 19 } }$

Question 5

Simplify the radical. Assume that all variables represent positive real numbers. $\sqrt { 44 x ^ { 7 } }$

Accepted Answer

A)  $4 x ^ { 6 } \sqrt { 11 x }$ 
B)  $2 \sqrt { 11 x ^ { 7 } }$ 
C)  $2 x ^ { 3 } \sqrt { 11 x }$ 
D)  $2 x \sqrt { 11 x ^ { 5 } }$ 
A)  $4 x ^ { 6 } \sqrt { 11 x }$ 
B)  $2 \sqrt { 11 x ^ { 7 } }$ 
C)  $2 x ^ { 3 } \sqrt { 11 x }$ 
D)  $2 x \sqrt { 11 x ^ { 5 } }$

Question 6

Simplify the expression. $$\sqrt { - 9 } \cdot \sqrt { - 64 }$$

Accepted Answer

The answer of Simplify the expression. \[\sqrt { - 9...

Question 7

Convert the expression to radical notation. $$a ^ { 5 / 7 } m ^ { 3 / 7 }$$

Accepted Answer

A)  $\sqrt [ 7 ] { a m }$ 
B)  $\sqrt [ 7 ] { a ^ { 5 } m ^ { 3 } }$ 
C)  $\sqrt { a m }$ 
D)  $\sqrt { a ^ { 5 } m ^ { 3 } }$ 
A)  $\sqrt [ 7 ] { a m }$ 
B)  $\sqrt [ 7 ] { a ^ { 5 } m ^ { 3 } }$ 
C)  $\sqrt { a m }$ 
D)  $\sqrt { a ^ { 5 } m ^ { 3 } }$

Question 8

Convert the expression to radical form and simplify. $25 ^ { 1 / 2 }$

Accepted Answer

A)  $\frac { 25 } { 2 }$ 
B)  625 
C)  5 
D)  Not a real number 
A)  $\frac { 25 } { 2 }$ 
B)  625 
C)  5 
D)  Not a real number

Question 9

Use a calculator to approximate the expression. Round to four decimal places, if necessary. $47 ^ { - 1 / 3 }$

Accepted Answer

A)  $0.3819$ 
B)  $0.2771$ 
C)  $6.8557$ 
D)  $3.6088$ 
A)  $0.3819$ 
B)  $0.2771$ 
C)  $6.8557$ 
D)  $3.6088$

Question 10

Evaluate the root without using a calculator or note that root is not a real number. $$\sqrt { 9 }$$

Accepted Answer

A)  81 
B)  -3 
C)  3 
D)  Not a real number 
A)  81 
B)  -3 
C)  3 
D)  Not a real number

Question 11

Simplify the radical. $\sqrt { 60 }$

Accepted Answer

A)  $4 \sqrt { 15 }$ 
B)  $\sqrt { 30 }$ 
C)  $2 \sqrt { 15 }$ 
D)  Cannot be simplified 
A)  $4 \sqrt { 15 }$ 
B)  $\sqrt { 30 }$ 
C)  $2 \sqrt { 15 }$ 
D)  Cannot be simplified

Question 12

Write the expression using rational exponents. Then simplify and convert back to radical notation. $\sqrt [ 6 ] { x ^ { 4 } }$

Accepted Answer

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

Question 13

Add or subtract the radical expressions as indicated, if possible. $$\sqrt [ 5 ] { 15 } + 8 \sqrt [ 5 ] { 15 } - \sqrt [ 5 ] { 7 }$$

Accepted Answer

A)  $8 \sqrt [ 5 ] { 23 }$ 
B)  $9 \sqrt [ 5 ] { 15 } - \sqrt [ 5 ] { 7 }$ 
C)  $8 \sqrt [ 5 ] { 8 }$ 
D)  Cannot be simplified further 
A)  $8 \sqrt [ 5 ] { 23 }$ 
B)  $9 \sqrt [ 5 ] { 15 } - \sqrt [ 5 ] { 7 }$ 
C)  $8 \sqrt [ 5 ] { 8 }$ 
D)  Cannot be simplified further

Question 14

Add or subtract the radical expressions as indicated, if possible. $$\sqrt [ 6 ] { 7 x } + \sqrt [ 5 ] { 7 x }$$

Accepted Answer

A)  $\sqrt [ 11 ] { 7 x }$ 
B)  $2 \sqrt [ 11 ] { 7 x }$ 
C)  $\sqrt [ 11 ] { 14 x }$ 
D)  Cannot be simplified further 
A)  $\sqrt [ 11 ] { 7 x }$ 
B)  $2 \sqrt [ 11 ] { 7 x }$ 
C)  $\sqrt [ 11 ] { 14 x }$ 
D)  Cannot be simplified further

Question 15

Multiply the radical expressions. $( \sqrt { 13 } + x ) ( \sqrt { 13 } - x )$

Accepted Answer

A)  $\sqrt { 13 } - x ^ { 2 }$ 
B)  $13 + x ^ { 2 }$ 
C)  $\sqrt { 26 } - x ^ { 2 }$ 
D)  $13 - x ^ { 2 }$ 
A)  $\sqrt { 13 } - x ^ { 2 }$ 
B)  $13 + x ^ { 2 }$ 
C)  $\sqrt { 26 } - x ^ { 2 }$ 
D)  $13 - x ^ { 2 }$

Question 16

Simplify the radical. $\sqrt [ 3 ] { 96 }$

Accepted Answer

A)  $8 \sqrt [ 3 ] { 48 }$ 
B)  $8 \sqrt [ 3 ] { 12 }$ 
C)  $2 \sqrt [ 3 ] { 96 }$ 
D)  $2 \sqrt [ 3 ] { 12 }$ 
A)  $8 \sqrt [ 3 ] { 48 }$ 
B)  $8 \sqrt [ 3 ] { 12 }$ 
C)  $2 \sqrt [ 3 ] { 96 }$ 
D)  $2 \sqrt [ 3 ] { 12 }$

Question 17

Simplify the expression, if possible. $- 27 ^ { - 4 / 3 }$

Accepted Answer

A)  $\frac { 1 } { 81 }$ 
B)  $- 81$ 
C)  81 
D)  $- \frac { 1 } { 81 }$ 
A)  $\frac { 1 } { 81 }$ 
B)  $- 81$ 
C)  81 
D)  $- \frac { 1 } { 81 }$

Question 18

Solve the equation. $$7 + \sqrt [ 4 ] { m } = 9$$

Accepted Answer

The answer of Solve the equation. \[7 + \sqrt [...

Question 19

Multiply. Write the answer in the form a + bi. $$( - 6 + 5 i ) ( 6 + 5 i )$$

Accepted Answer

A)  $- 61 + 60 i$ 
B)  $- 61 + 0 i$ 
C)  $61 + 0 i$ 
D)  $61 - 60 i$ 
A)  $- 61 + 60 i$ 
B)  $- 61 + 0 i$ 
C)  $61 + 0 i$ 
D)  $61 - 60 i$

Question 20

Which two radicals are like?

Accepted Answer

A)  $\sqrt [ 4 ] { 108 }$ and $- \sqrt [ 3 ] { 108 }$ 
B)  $\sqrt { 108 }$ and $- 2 \sqrt { 3 }$ 
C)  $\sqrt [ 3 ] { - 22 }$ and $\sqrt [ 3 ] { 44 }$ 
D)  $\sqrt { x ^ { 2 } }$ and $\sqrt { y ^ { 2 } }$ 
A)  $\sqrt [ 4 ] { 108 }$ and $- \sqrt [ 3 ] { 108 }$ 
B)  $\sqrt { 108 }$ and $- 2 \sqrt { 3 }$ 
C)  $\sqrt [ 3 ] { - 22 }$ and $\sqrt [ 3 ] { 44 }$ 
D)  $\sqrt { x ^ { 2 } }$ and $\sqrt { y ^ { 2 } }$

Solve the equation. $- 4 + \sqrt { 3 x + 5 } = 3$

Simplify the radical. $\sqrt [ 4 ] { q ^ { 13 } }$

Rationalize the denominator and simplify completely. $\sqrt { \frac { x ^ { 3 } } { 19 } }$

Simplify the radical. Assume that all variables represent positive real numbers. $\sqrt { 44 x ^ { 7 } }$

Simplify the expression. $\sqrt { - 9 } \cdot \sqrt { - 64 }$

Convert the expression to radical notation. $a ^ { 5 / 7 } m ^ { 3 / 7 }$

Convert the expression to radical form and simplify. $25 ^ { 1 / 2 }$

Use a calculator to approximate the expression. Round to four decimal places, if necessary. $47 ^ { - 1 / 3 }$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt { 9 }$

Simplify the radical. $\sqrt { 60 }$

Write the expression using rational exponents. Then simplify and convert back to radical notation. $\sqrt [ 6 ] { x ^ { 4 } }$

Add or subtract the radical expressions as indicated, if possible. $\sqrt [ 5 ] { 15 } + 8 \sqrt [ 5 ] { 15 } - \sqrt [ 5 ] { 7 }$

Add or subtract the radical expressions as indicated, if possible. $\sqrt [ 6 ] { 7 x } + \sqrt [ 5 ] { 7 x }$

Multiply the radical expressions. $( \sqrt { 13 } + x ) ( \sqrt { 13 } - x )$

Simplify the radical. $\sqrt [ 3 ] { 96 }$

Simplify the expression, if possible. $- 27 ^ { - 4 / 3 }$

Solve the equation. $7 + \sqrt [ 4 ] { m } = 9$

Multiply. Write the answer in the form a + bi. $( - 6 + 5 i ) ( 6 + 5 i )$

Which two radicals are like?

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Exam 6: Radicals and Complex Numbers

Solve the equation. −4+3x+5=3- 4 + \sqrt { 3 x + 5 } = 3−4+3x+5​=3

Simplify the radical. q134\sqrt [ 4 ] { q ^ { 13 } }4q13​

Rationalize the denominator and simplify completely. x319\sqrt { \frac { x ^ { 3 } } { 19 } }19x3​​

Simplify the radical. Assume that all variables represent positive real numbers. 44x7\sqrt { 44 x ^ { 7 } }44x7​

Simplify the expression. −9⋅−64\sqrt { - 9 } \cdot \sqrt { - 64 }−9​⋅−64​

Convert the expression to radical notation. a5/7m3/7a ^ { 5 / 7 } m ^ { 3 / 7 }a5/7m3/7

Convert the expression to radical form and simplify. 251/225 ^ { 1 / 2 }251/2

Use a calculator to approximate the expression. Round to four decimal places, if necessary. 47−1/347 ^ { - 1 / 3 }47−1/3

Evaluate the root without using a calculator or note that root is not a real number. 9\sqrt { 9 }9​

Simplify the radical. 60\sqrt { 60 }60​

Write the expression using rational exponents. Then simplify and convert back to radical notation. x46\sqrt [ 6 ] { x ^ { 4 } }6x4​

Add or subtract the radical expressions as indicated, if possible. 155+8155−75\sqrt [ 5 ] { 15 } + 8 \sqrt [ 5 ] { 15 } - \sqrt [ 5 ] { 7 }515​+8515​−57​

Add or subtract the radical expressions as indicated, if possible. 7x6+7x5\sqrt [ 6 ] { 7 x } + \sqrt [ 5 ] { 7 x }67x​+57x​

Multiply the radical expressions. (13+x)(13−x)( \sqrt { 13 } + x ) ( \sqrt { 13 } - x )(13​+x)(13​−x)

Simplify the radical. 963\sqrt [ 3 ] { 96 }396​

Simplify the expression, if possible. −27−4/3- 27 ^ { - 4 / 3 }−27−4/3

Solve the equation. 7+m4=97 + \sqrt [ 4 ] { m } = 97+4m​=9

Multiply. Write the answer in the form a + bi. (−6+5i)(6+5i)( - 6 + 5 i ) ( 6 + 5 i )(−6+5i)(6+5i)

Which two radicals are like?

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Solve the equation. $- 4 + \sqrt { 3 x + 5 } = 3$

Simplify the radical. $\sqrt [ 4 ] { q ^ { 13 } }$

Rationalize the denominator and simplify completely. $\sqrt { \frac { x ^ { 3 } } { 19 } }$

Simplify the radical. Assume that all variables represent positive real numbers. $\sqrt { 44 x ^ { 7 } }$

Simplify the expression. $\sqrt { - 9 } \cdot \sqrt { - 64 }$

Convert the expression to radical notation. $a ^ { 5 / 7 } m ^ { 3 / 7 }$

Convert the expression to radical form and simplify. $25 ^ { 1 / 2 }$

Use a calculator to approximate the expression. Round to four decimal places, if necessary. $47 ^ { - 1 / 3 }$

Evaluate the root without using a calculator or note that root is not a real number. $\sqrt { 9 }$

Simplify the radical. $\sqrt { 60 }$

Write the expression using rational exponents. Then simplify and convert back to radical notation. $\sqrt [ 6 ] { x ^ { 4 } }$

Add or subtract the radical expressions as indicated, if possible. $\sqrt [ 5 ] { 15 } + 8 \sqrt [ 5 ] { 15 } - \sqrt [ 5 ] { 7 }$

Add or subtract the radical expressions as indicated, if possible. $\sqrt [ 6 ] { 7 x } + \sqrt [ 5 ] { 7 x }$

Multiply the radical expressions. $( \sqrt { 13 } + x ) ( \sqrt { 13 } - x )$

Simplify the radical. $\sqrt [ 3 ] { 96 }$

Simplify the expression, if possible. $- 27 ^ { - 4 / 3 }$

Solve the equation. $7 + \sqrt [ 4 ] { m } = 9$

Multiply. Write the answer in the form a + bi. $( - 6 + 5 i ) ( 6 + 5 i )$