Question 1

Write the expression as a single radical. $\sqrt { \sqrt [ 14 ] { x } }$

Accepted Answer

A)  $28 \sqrt { x }$ 
B)  $\sqrt [ 7 ] { x }$ 
C)  $\sqrt { x ^ { 7 } }$ 
D)  $\sqrt [ 28 ] { x }$ 
A)  $28 \sqrt { x }$ 
B)  $\sqrt [ 7 ] { x }$ 
C)  $\sqrt { x ^ { 7 } }$ 
D)  $\sqrt [ 28 ] { x }$

Question 2

Find the exact area.

Accepted Answer

A)  $405 \sqrt { 3 }$ 
B)  $45 \sqrt { 5 }$ 
C)  $45 \sqrt { 3 }$ 
D)  $405 \sqrt { 5 }$ 
A)  $405 \sqrt { 3 }$ 
B)  $45 \sqrt { 5 }$ 
C)  $45 \sqrt { 3 }$ 
D)  $405 \sqrt { 5 }$

Question 3

Multiply the radical expressions. $- 4 \sqrt [ 3 ] { 4 } \cdot 6 \sqrt [ 3 ] { 6 }$

Accepted Answer

A)  $2 \sqrt [ 3 ] { 10 }$ 
B)  $- 48 \sqrt [ 3 ] { 6 }$ 
C)  $- 192 \sqrt [ 3 ] { 3 }$ 
D)  $- 48 \sqrt [ 3 ] { 3 }$ 
A)  $2 \sqrt [ 3 ] { 10 }$ 
B)  $- 48 \sqrt [ 3 ] { 6 }$ 
C)  $- 192 \sqrt [ 3 ] { 3 }$ 
D)  $- 48 \sqrt [ 3 ] { 3 }$

Question 4

Rationalize the denominator and simplify completely. $\sqrt [ 4 ] { \frac { 81 } { 2 } }$

Accepted Answer

A)  $\frac { 3 \sqrt [ 4 ] { 8 } } { 2 }$ 
B)  $\frac { 9 \sqrt [ 4 ] { 2 } } { 2 }$ 
C)  $\frac { 9 \sqrt [ 4 ] { 8 } } { 2 }$ 
D)  $\frac { 3 \sqrt [ 4 ] { 2 } } { 2 }$ 
A)  $\frac { 3 \sqrt [ 4 ] { 8 } } { 2 }$ 
B)  $\frac { 9 \sqrt [ 4 ] { 2 } } { 2 }$ 
C)  $\frac { 9 \sqrt [ 4 ] { 8 } } { 2 }$ 
D)  $\frac { 3 \sqrt [ 4 ] { 2 } } { 2 }$

Question 5

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $$h ^ { 7 / 3 } \cdot h ^ { 5 / 3 }$$

Accepted Answer

A)  $h ^ { 35 / 3 }$ 
B)  $h ^ { 35 / 9 }$ 
C)  $h ^ { 4 }$ 
D)  $h ^ { 2 }$ 
A)  $h ^ { 35 / 3 }$ 
B)  $h ^ { 35 / 9 }$ 
C)  $h ^ { 4 }$ 
D)  $h ^ { 2 }$

Question 6

Two mountain bikers take off from the same place at the same time. One travels north at 4 mph, and the other travels east at 3 mph. How far apart are they after 4 hr?

Accepted Answer

A)  20 mi 
B)  5 mi 
C)  14 mi 
D)  28 mi 
A)  20 mi 
B)  5 mi 
C)  14 mi 
D)  28 mi

Question 7

Solve for y. $$x + \sqrt [ 3 ] { y z } = m$$

Accepted Answer

A)  $y = \frac { 3 m - 3 x } { z }$ 
B)  $y = \frac { ( m - x ) ^ { 3 } } { z }$ 
C)  $y = \frac { ( m - x ) ^ { 3 } } { \sqrt [ 3 ] { z } }$ 
D)  $y = \frac { m ^ { 3 } - x ^ { 3 } } { z }$ 
A)  $y = \frac { 3 m - 3 x } { z }$ 
B)  $y = \frac { ( m - x ) ^ { 3 } } { z }$ 
C)  $y = \frac { ( m - x ) ^ { 3 } } { \sqrt [ 3 ] { z } }$ 
D)  $y = \frac { m ^ { 3 } - x ^ { 3 } } { z }$

Question 8

Rationalize the numerator by multiplying both numerator and denominator by the conjugate of the numerator. $\frac { \sqrt { 2 } + 4 } { 5 }$

Accepted Answer

A)  $\frac { - 14 } { \sqrt { 2 } - 4 }$ 
B)  $\frac { - 14 } { 5 \sqrt { 2 } - 20 }$ 
C)  $\frac { 18 } { \sqrt { 2 } - 4 }$ 
D)  $\frac { 18 } { 5 \sqrt { 2 } - 20 }$ 
A)  $\frac { - 14 } { \sqrt { 2 } - 4 }$ 
B)  $\frac { - 14 } { 5 \sqrt { 2 } - 20 }$ 
C)  $\frac { 18 } { \sqrt { 2 } - 4 }$ 
D)  $\frac { 18 } { 5 \sqrt { 2 } - 20 }$

Write the expression as a single radical. $\sqrt { \sqrt [ 14 ] { x } }$

Find the exact area.

Multiply the radical expressions. $- 4 \sqrt [ 3 ] { 4 } \cdot 6 \sqrt [ 3 ] { 6 }$

Rationalize the denominator and simplify completely. $\sqrt [ 4 ] { \frac { 81 } { 2 } }$

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $h ^ { 7 / 3 } \cdot h ^ { 5 / 3 }$

Two mountain bikers take off from the same place at the same time. One travels north at 4 mph, and the other travels east at 3 mph. How far apart are they after 4 hr?

Solve for y. $x + \sqrt [ 3 ] { y z } = m$

Rationalize the numerator by multiplying both numerator and denominator by the conjugate of the numerator. $\frac { \sqrt { 2 } + 4 } { 5 }$

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

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Exam 6: Radicals and Complex Numbers

Write the expression as a single radical. x14\sqrt { \sqrt [ 14 ] { x } }14x​​

Find the exact area.

Multiply the radical expressions. −443⋅663- 4 \sqrt [ 3 ] { 4 } \cdot 6 \sqrt [ 3 ] { 6 }−434​⋅636​

Rationalize the denominator and simplify completely. 8124\sqrt [ 4 ] { \frac { 81 } { 2 } }4281​​

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. h7/3⋅h5/3h ^ { 7 / 3 } \cdot h ^ { 5 / 3 }h7/3⋅h5/3

Two mountain bikers take off from the same place at the same time. One travels north at 4 mph, and the other travels east at 3 mph. How far apart are they after 4 hr?

Solve for y. x+yz3=mx + \sqrt [ 3 ] { y z } = mx+3yz​=m

Rationalize the numerator by multiplying both numerator and denominator by the conjugate of the numerator. 2+45\frac { \sqrt { 2 } + 4 } { 5 }52​+4​

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

Write the expression as a single radical. $\sqrt { \sqrt [ 14 ] { x } }$

Multiply the radical expressions. $- 4 \sqrt [ 3 ] { 4 } \cdot 6 \sqrt [ 3 ] { 6 }$

Rationalize the denominator and simplify completely. $\sqrt [ 4 ] { \frac { 81 } { 2 } }$

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. $h ^ { 7 / 3 } \cdot h ^ { 5 / 3 }$

Solve for y. $x + \sqrt [ 3 ] { y z } = m$

Rationalize the numerator by multiplying both numerator and denominator by the conjugate of the numerator. $\frac { \sqrt { 2 } + 4 } { 5 }$