Question 1

Solve.
-$\sqrt [ 3 ] { 4 x + 5 } - 4 = 0$

Accepted Answer

A)  12 
B)  $\frac { 59 } { 4 }$ 
C)  $\frac { 11 } { 4 }$ 
D)  16 
A)  12 
B)  $\frac { 59 } { 4 }$ 
C)  $\frac { 11 } { 4 }$ 
D)  16

Question 2

Use the product rule to multiply. Assume all variables represent positive real numbers.
-$\sqrt { \frac { x } { 3 } } \cdot \sqrt { \frac { y } { 2 } }$

Accepted Answer

A)  $\sqrt { \frac { x y } { 6 } }$ 
B)  $\frac { x y } { 6 }$ 
C)  $\sqrt { \frac { 2 x + 3 y } { 6 } }$ 
D)  $\sqrt { \frac { 2 x } { 3 y } }$ 
A)  $\sqrt { \frac { x y } { 6 } }$ 
B)  $\frac { x y } { 6 }$ 
C)  $\sqrt { \frac { 2 x + 3 y } { 6 } }$ 
D)  $\sqrt { \frac { 2 x } { 3 y } }$

Question 3

Use radical notation to write the expression. Simplify if possible.
-$64 ^ { 4 / 3 }$

Accepted Answer

A)  16,384 
B)  4096 
C)  1024 
D)  256 
A)  16,384 
B)  4096 
C)  1024 
D)  256

Question 4

Rationalize the numerator and simplify. Assume all variables represent positive real numbers.
-$\frac { \sqrt { 17 } } { 5 \mathrm { z } }$

Accepted Answer

A)  $\frac { 17 } { 25 \mathrm { z } \sqrt { 17 } }$ 
B)  $\frac { 17 } { 5 z \sqrt { 17 } }$ 
C)  $\frac { 1 } { 294 }$ 
D)  $\frac { 1 } { 5 \mathrm { z } \sqrt { 17 } }$ 
A)  $\frac { 17 } { 25 \mathrm { z } \sqrt { 17 } }$ 
B)  $\frac { 17 } { 5 z \sqrt { 17 } }$ 
C)  $\frac { 1 } { 294 }$ 
D)  $\frac { 1 } { 5 \mathrm { z } \sqrt { 17 } }$

Question 5

Solve.
-$\sqrt [ 3 ] { x + 3 } + 4 = 0$

Accepted Answer

A)  13 
B)  16 
C)  $- 64$ 
D)  $- 67$ 
A)  13 
B)  16 
C)  $- 64$ 
D)  $- 67$

Question 6

Use radical notation to write the expression. Simplify if possible.
-$\left( \frac { 8 } { 64 } \right) ^ { 2 / 3 }$

Accepted Answer

A)  $\frac { 1 } { 6 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $- \frac { 1 } { 4 }$ 
A)  $\frac { 1 } { 6 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $- \frac { 1 } { 4 }$

Question 7

Find the cube root.
-$\sqrt [ 3 ] { \frac { x ^ { 12 } } { 125 y ^ { 6 } } }$

Accepted Answer

A)  $\frac { x ^ { 4 } } { 5 y ^ { 2 } }$ 
B)  $\frac { x ^ { 4 } } { 25 y ^ { 2 } }$ 
C)  $\frac { 5 y ^ { 2 } } { x ^ { 4 } }$ 
D)  $\frac { x ^ { 3 } } { 5 y ^ { 3 } }$ 
A)  $\frac { x ^ { 4 } } { 5 y ^ { 2 } }$ 
B)  $\frac { x ^ { 4 } } { 25 y ^ { 2 } }$ 
C)  $\frac { 5 y ^ { 2 } } { x ^ { 4 } }$ 
D)  $\frac { x ^ { 3 } } { 5 y ^ { 3 } }$

Question 8

Perform the indicated operation. Write the result in the form a + bi.
-$\frac { 8 + 7 i } { 5 + 6 i }$

Accepted Answer

A)  $- \frac { 2 } { 61 } - \frac { 83 } { 61 } \mathrm { i }$ 
B)  $\frac { 82 } { 61 } - \frac { 13 } { 61 } \mathrm { i }$ 
C)  $\frac { 2 } { 11 } + \frac { 13 } { 11 } \mathrm { i }$ 
D)  $- \frac { 82 } { 11 } + \frac { 13 } { 11 } \mathrm { i }$ 
A)  $- \frac { 2 } { 61 } - \frac { 83 } { 61 } \mathrm { i }$ 
B)  $\frac { 82 } { 61 } - \frac { 13 } { 61 } \mathrm { i }$ 
C)  $\frac { 2 } { 11 } + \frac { 13 } { 11 } \mathrm { i }$ 
D)  $- \frac { 82 } { 11 } + \frac { 13 } { 11 } \mathrm { i }$

Question 9

Perform the indicated operations. Assume that all variables represent positive numbers.
-$\sqrt { 12 x ^ { 3 } } - 8 \sqrt { 108 x ^ { 3 } }$

Accepted Answer

A)  $- 8 \sqrt { - 96 x ^ { 3 } }$ 
B)  $- 46 x \sqrt { 3 x }$ 
C)  $50 x \sqrt { 3 x }$ 
D)  $- 46 \sqrt { 3 x ^ { 3 } }$ 
A)  $- 8 \sqrt { - 96 x ^ { 3 } }$ 
B)  $- 46 x \sqrt { 3 x }$ 
C)  $50 x \sqrt { 3 x }$ 
D)  $- 46 \sqrt { 3 x ^ { 3 } }$

Question 10

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l } 
\text { index rationalizing } & \text { conjugate } & \text { principal square rootcube root midpoint } \
\text { complex numberlike radicals } & \text { radicand } & \text { imaginary unit } \quad \text { distance }
\end{array}$$
-The ----------written i, is the number whose square is -1.

Accepted Answer

A)  conjugate 
B)  imaginary unit 
C)  complex number 
D)  radicand 
A)  conjugate 
B)  imaginary unit 
C)  complex number 
D)  radicand

Question 11

Use the product rule to multiply. Assume all variables represent positive real numbers.
-$\sqrt { 18 } \cdot \sqrt { 50 }$

Accepted Answer

A)  30 
B)  15 
C)  $15 \sqrt { 2 }$ 
D)  50 
A)  30 
B)  15 
C)  $15 \sqrt { 2 }$ 
D)  50

Question 12

Rationalize the numerator and simplify. Assume all variables represent positive real numbers.
-$\sqrt { \frac { 7 } { 2 } }$

Accepted Answer

A)  $\frac { 7 } { \sqrt { 14 } }$ 
B)  $\frac { 7 } { \sqrt { 2 } }$ 
C)  $\frac { 2 } { \sqrt { 2 } }$ 
D)  $\frac { \sqrt { 14 } } { 2 }$ 
A)  $\frac { 7 } { \sqrt { 14 } }$ 
B)  $\frac { 7 } { \sqrt { 2 } }$ 
C)  $\frac { 2 } { \sqrt { 2 } }$ 
D)  $\frac { \sqrt { 14 } } { 2 }$

Question 13

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$( \sqrt { 11 x } - 5 \sqrt { 2 } ) ( \sqrt { 11 x } - 5 \sqrt { 5 } )$

Accepted Answer

A)  $121 x ^ { 2 } - 5 \sqrt { 55 x } - 5 \sqrt { 22 x } + 25 \sqrt { 10 }$ 
B)  $11 x - 5 \sqrt { 110 x } + 25 \sqrt { 10 }$ 
C)  $11 x - 5 \sqrt { 55 x } - 5 \sqrt { 22 x } + 25 \sqrt { 10 }$ 
D)  $11 x - 5 \sqrt { 55 x } - 5 \sqrt { 22 x } + 25 \sqrt { 2 }$ 
A)  $121 x ^ { 2 } - 5 \sqrt { 55 x } - 5 \sqrt { 22 x } + 25 \sqrt { 10 }$ 
B)  $11 x - 5 \sqrt { 110 x } + 25 \sqrt { 10 }$ 
C)  $11 x - 5 \sqrt { 55 x } - 5 \sqrt { 22 x } + 25 \sqrt { 10 }$ 
D)  $11 x - 5 \sqrt { 55 x } - 5 \sqrt { 22 x } + 25 \sqrt { 2 }$

Question 14

Add or subtract. Assume all variables represent positive real numbers.
-$18 \sqrt [ 3 ] { 2 } - 3 \sqrt [ 3 ] { 54 }$

Accepted Answer

A)  $15 \sqrt [ 3 ] { 2 }$ 
B)  $18 \sqrt [ 3 ] { 2 } - 3 \sqrt [ 3 ] { 54 }$ 
C)  $9 \sqrt [ 3 ] { 2 }$ 
D)  $- 9 \sqrt [ 3 ] { 2 }$ 
A)  $15 \sqrt [ 3 ] { 2 }$ 
B)  $18 \sqrt [ 3 ] { 2 } - 3 \sqrt [ 3 ] { 54 }$ 
C)  $9 \sqrt [ 3 ] { 2 }$ 
D)  $- 9 \sqrt [ 3 ] { 2 }$

Question 15

Use radical notation to write the expression. Simplify if possible.
-$256 ^ { 1 / 4 }$

Accepted Answer

A)  16 
B)  64 
C)  1024 
D)  4 
A)  16 
B)  64 
C)  1024 
D)  4

Question 16

Use the product rule to multiply. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { 8 m ^ { 3 } } \cdot \sqrt [ 3 ] { 27 m ^ { 3 } }$

Accepted Answer

A)  $5 \mathrm {~m}$ 
B)  6 
C)  $6 \mathrm {~m} ^ { 2 }$ 
D)  $- 2 m$ 
A)  $5 \mathrm {~m}$ 
B)  6 
C)  $6 \mathrm {~m} ^ { 2 }$ 
D)  $- 2 m$

Question 17

Solve.
-$\sqrt { x ^ { 2 } - 3 x + 54 } = x + 3$

Accepted Answer

A)  $- 5$ 
B)  8 
C)  2 
D)  5 
A)  $- 5$ 
B)  8 
C)  2 
D)  5

Question 18

Use the quotient rule to divide and simplify.
-$\frac { \sqrt { 54 x ^ { 11 } } } { \sqrt { 6 x } }$

Accepted Answer

A)  $x ^ { 5 } \sqrt { 6 }$ 
B)  $3 x ^ { 5 }$ 
C)  $3 x ^ { 5 } \sqrt { x }$ 
D)  $x ^ { 5 } \sqrt { 3 }$ 
A)  $x ^ { 5 } \sqrt { 6 }$ 
B)  $3 x ^ { 5 }$ 
C)  $3 x ^ { 5 } \sqrt { x }$ 
D)  $x ^ { 5 } \sqrt { 3 }$

Question 19

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\frac { 15 } { \sqrt { 5 x } }$

Accepted Answer

A)  $\frac { 3 \sqrt { 5 x } } { x }$ 
B)  $\frac { 15 \sqrt { x } } { x }$ 
C)  $\frac { 15 \sqrt { 5 x } } { 5 x }$ 
D)  $\frac { 3 \sqrt { 5 x } } { 5 x }$ 
A)  $\frac { 3 \sqrt { 5 x } } { x }$ 
B)  $\frac { 15 \sqrt { x } } { x }$ 
C)  $\frac { 15 \sqrt { 5 x } } { 5 x }$ 
D)  $\frac { 3 \sqrt { 5 x } } { 5 x }$

Question 20

Perform the indicated operation and simplify. Write the result in the form a $a + bi$
-$\frac { 9 + 2 i } { 4 - 6 i }$

Accepted Answer

A)  $- \frac { 12 } { 5 } + \frac { 31 } { 20 } \mathrm { i }$ 
B)  $\frac { 24 } { 13 } + \frac { 23 } { 13 } \mathrm { i }$ 
C)  $- \frac { 3 } { 5 } + \frac { 31 } { 20 } \mathrm { i }$ 
D)  $\frac { 6 } { 13 } + \frac { 31 } { 26 } \mathrm { i }$ 
A)  $- \frac { 12 } { 5 } + \frac { 31 } { 20 } \mathrm { i }$ 
B)  $\frac { 24 } { 13 } + \frac { 23 } { 13 } \mathrm { i }$ 
C)  $- \frac { 3 } { 5 } + \frac { 31 } { 20 } \mathrm { i }$ 
D)  $\frac { 6 } { 13 } + \frac { 31 } { 26 } \mathrm { i }$

Solve. - $\sqrt [ 3 ] { 4 x + 5 } - 4 = 0$

Use the product rule to multiply. Assume all variables represent positive real numbers. - $\sqrt { \frac { x } { 3 } } \cdot \sqrt { \frac { y } { 2 } }$

Use radical notation to write the expression. Simplify if possible. - $64 ^ { 4 / 3 }$

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - $\frac { \sqrt { 17 } } { 5 \mathrm { z } }$

Solve. - $\sqrt [ 3 ] { x + 3 } + 4 = 0$

Use radical notation to write the expression. Simplify if possible. - $\left( \frac { 8 } { 64 } \right) ^ { 2 / 3 }$

Find the cube root. - $\sqrt [ 3 ] { \frac { x ^ { 12 } } { 125 y ^ { 6 } } }$

Perform the indicated operation. Write the result in the form a + bi. - $\frac { 8 + 7 i } { 5 + 6 i }$

Perform the indicated operations. Assume that all variables represent positive numbers. - $\sqrt { 12 x ^ { 3 } } - 8 \sqrt { 108 x ^ { 3 } }$

Fill in the blank with one of the words or phrases listed below. index rationalizing conjugate principal square rootcube root midpoint complex numberlike radicals radicand imaginary unit distance -The ----------written i, is the number whose square is -1.

Use the product rule to multiply. Assume all variables represent positive real numbers. - $\sqrt { 18 } \cdot \sqrt { 50 }$

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - $\sqrt { \frac { 7 } { 2 } }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( \sqrt { 11 x } - 5 \sqrt { 2 } ) ( \sqrt { 11 x } - 5 \sqrt { 5 } )$

Add or subtract. Assume all variables represent positive real numbers. - $18 \sqrt [ 3 ] { 2 } - 3 \sqrt [ 3 ] { 54 }$

Use radical notation to write the expression. Simplify if possible. - $256 ^ { 1 / 4 }$

Use the product rule to multiply. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 8 m ^ { 3 } } \cdot \sqrt [ 3 ] { 27 m ^ { 3 } }$

Solve. - $\sqrt { x ^ { 2 } - 3 x + 54 } = x + 3$

Use the quotient rule to divide and simplify. - $\frac { \sqrt { 54 x ^ { 11 } } } { \sqrt { 6 x } }$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\frac { 15 } { \sqrt { 5 x } }$

Perform the indicated operation and simplify. Write the result in the form a $a + bi$ - $\frac { 9 + 2 i } { 4 - 6 i }$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 10: Rational Exponents, Radicals, and Complex Numbers

Solve. - 4x+53−4=0\sqrt [ 3 ] { 4 x + 5 } - 4 = 034x+5​−4=0

Use the product rule to multiply. Assume all variables represent positive real numbers. - x3⋅y2\sqrt { \frac { x } { 3 } } \cdot \sqrt { \frac { y } { 2 } }3x​​⋅2y​​

Use radical notation to write the expression. Simplify if possible. - 644/364 ^ { 4 / 3 }644/3

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - 175z\frac { \sqrt { 17 } } { 5 \mathrm { z } }5z17​​

Solve. - x+33+4=0\sqrt [ 3 ] { x + 3 } + 4 = 03x+3​+4=0

Use radical notation to write the expression. Simplify if possible. - (864)2/3\left( \frac { 8 } { 64 } \right) ^ { 2 / 3 }(648​)2/3

Find the cube root. - x12125y63\sqrt [ 3 ] { \frac { x ^ { 12 } } { 125 y ^ { 6 } } }3125y6x12​​

Perform the indicated operation. Write the result in the form a + bi. - 8+7i5+6i\frac { 8 + 7 i } { 5 + 6 i }5+6i8+7i​

Perform the indicated operations. Assume that all variables represent positive numbers. - 12x3−8108x3\sqrt { 12 x ^ { 3 } } - 8 \sqrt { 108 x ^ { 3 } }12x3​−8108x3​