Question 1

Divide.
-$\frac { \sqrt { - 1000 } \sqrt { - 8 } } { \sqrt { - 25 } }$

Accepted Answer

A)  $8 \sqrt { 5 }$ 
B)  $- 8 i \sqrt { 5 }$ 
C)  $- 8 \sqrt { 5 }$ 
D)  $8 i \sqrt { 5 }$ 
A)  $8 \sqrt { 5 }$ 
B)  $- 8 i \sqrt { 5 }$ 
C)  $- 8 \sqrt { 5 }$ 
D)  $8 i \sqrt { 5 }$ D

Question 2

Simplify.
-$( \sqrt { 10 } + \sqrt { 2 } ) ( \sqrt { 10 } - \sqrt { 2 } )$

Accepted Answer

A)  $10 - 2 \sqrt { 2 }$ 
B) 8 
C)  $10 - 2 \sqrt { 10 }$ 
D) 12 
A)  $10 - 2 \sqrt { 2 }$ 
B) 8 
C)  $10 - 2 \sqrt { 10 }$ 
D) 12 B

Question 3

Simplify.
-$\frac { \sqrt { 7 } } { 7 } + \frac { 2 } { \sqrt { 7 } } + \sqrt { 28 }$

Accepted Answer

A)  $\frac { 16 \sqrt { 7 } } { 7 }$ 
B)  $\frac { 17 \sqrt { 7 } } { 7 }$ 
C) 119 
D)  $\frac { 3 } { 7 } + 2 \sqrt { 7 }$ 
A)  $\frac { 16 \sqrt { 7 } } { 7 }$ 
B)  $\frac { 17 \sqrt { 7 } } { 7 }$ 
C) 119 
D)  $\frac { 3 } { 7 } + 2 \sqrt { 7 }$ B

Question 4

Evaluate if possible. If the expression is not a real number, so state.
-$27 ^ { - 1 / 3 }$

Accepted Answer

A) -3 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 27 }$ 
D)  $- \frac { 1 } { 3 }$ 
A) -3 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 27 }$ 
D)  $- \frac { 1 } { 3 }$

Question 5

Solve and check your solution(s). If the equation has no real solution, so state.
-$\sqrt { 6 x - 5 } = 5$

Accepted Answer

A)  $\frac { 25 } { 6 }$ 
B) 25 
C) 5 
D)  $\frac { 10 } { 3 }$ 
A)  $\frac { 25 } { 6 }$ 
B) 25 
C) 5 
D)  $\frac { 10 } { 3 }$

Question 6

Simplify. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { \frac { 7 } { 3 } }$

Accepted Answer

A)  $\frac { 63 } { 3 }$ 
B)  $\frac { \sqrt [ 3 ] { 63 } } { 3 }$ 
C)  $\frac { \sqrt [ 3 ] { 189 } } { 3 }$ 
D)  $\frac { \sqrt [ 3 ] { 21 } } { 3 }$ 
A)  $\frac { 63 } { 3 }$ 
B)  $\frac { \sqrt [ 3 ] { 63 } } { 3 }$ 
C)  $\frac { \sqrt [ 3 ] { 189 } } { 3 }$ 
D)  $\frac { \sqrt [ 3 ] { 21 } } { 3 }$

Question 7

Simplify.
-$5 \sqrt [ 3 ] { x ^ { 2 } } \left( \sqrt [ 3 ] { 25 x } - \sqrt [ 3 ] { 25 x ^ { 8 } } \right)$

Accepted Answer

A)  $25 x - 5 x ^ { 9 } \sqrt [ 3 ] { 25 }$ 
B)  $25 x - 5 x ^ { 3 } \sqrt [ 3 ] { 5 x }$ 
C)  $5 x \sqrt [ 3 ] { 25 } - 5 x ^ { 3 } \sqrt [ 3 ] { 25 x }$ 
D)  $5 x \sqrt [ 3 ] { 25 x } - 5 x ^ { 3 } \sqrt [ 3 ] { 5 }$ 
A)  $25 x - 5 x ^ { 9 } \sqrt [ 3 ] { 25 }$ 
B)  $25 x - 5 x ^ { 3 } \sqrt [ 3 ] { 5 x }$ 
C)  $5 x \sqrt [ 3 ] { 25 } - 5 x ^ { 3 } \sqrt [ 3 ] { 25 x }$ 
D)  $5 x \sqrt [ 3 ] { 25 x } - 5 x ^ { 3 } \sqrt [ 3 ] { 5 }$

Question 8

Simplify.
-$3 \sqrt [ 3 ] { 256 x } - 4 \sqrt [ 3 ] { 108 x }$

Accepted Answer

A)  $12 \sqrt [ 3 ] { x } - 4 \sqrt [ 3 ] { 108 x }$ 
B)  $3 \sqrt [ 3 ] { 256 x } - 4 \sqrt [ 3 ] { 108 x }$ 
C) 0 
D)  $36 \sqrt [ 3 ] { x }$ 
A)  $12 \sqrt [ 3 ] { x } - 4 \sqrt [ 3 ] { 108 x }$ 
B)  $3 \sqrt [ 3 ] { 256 x } - 4 \sqrt [ 3 ] { 108 x }$ 
C) 0 
D)  $36 \sqrt [ 3 ] { x }$

Question 9

Simplify.
-$\sqrt [ 3 ] { \mathrm { p } ^ { 32 } }$

Accepted Answer

A)  $\mathrm { p } \sqrt [ 3 ] { \mathrm { p } ^ { 29 } }$ 
B)  $p ^ { 12 }$ 
C)  $\sqrt [ 3 ] { \mathrm { p } ^ { 32 } }$ 
D)  $p ^ { 10 } \sqrt [ 3 ] { p ^ { 2 } }$ 
A)  $\mathrm { p } \sqrt [ 3 ] { \mathrm { p } ^ { 29 } }$ 
B)  $p ^ { 12 }$ 
C)  $\sqrt [ 3 ] { \mathrm { p } ^ { 32 } }$ 
D)  $p ^ { 10 } \sqrt [ 3 ] { p ^ { 2 } }$

Question 10

Evaluate.
-$\mathrm { i } ^ { 21 }$

Accepted Answer

A) 1 
B) -1 
C) i 
D) -i 
A) 1 
B) -1 
C) i 
D) -i

Question 11

Multiply. Write the result in the form a + bi.
-$\left( \frac { 1 } { 3 } - \frac { 1 } { 2 } \mathrm { i } \right) \left( \frac { 3 } { 5 } - \frac { 3 } { 5 } \mathrm { i } \right)$

Accepted Answer

A)  $- \frac { 13 } { 10 } - \frac { 33 } { 10 } \mathrm { i }$ 
B)  $\frac { 1 } { 2 } - \frac { 1 } { 2 } \mathrm { i }$ 
C)  $- \frac { 1 } { 10 } + \frac { 1 } { 2 } \mathrm { i }$ 
D)  $- \frac { 1 } { 10 } - \frac { 1 } { 2 } i$ 
A)  $- \frac { 13 } { 10 } - \frac { 33 } { 10 } \mathrm { i }$ 
B)  $\frac { 1 } { 2 } - \frac { 1 } { 2 } \mathrm { i }$ 
C)  $- \frac { 1 } { 10 } + \frac { 1 } { 2 } \mathrm { i }$ 
D)  $- \frac { 1 } { 10 } - \frac { 1 } { 2 } i$

Question 12

Simplify.
-3 - 6 108 + 3 300

Accepted Answer

A) -5 3 
B) -5 411 
C) -3 3 
D) -3 411 
A) -5 3 
B) -5 411 
C) -3 3 
D) -3 411

Question 13

Simplify.
-$\sqrt [ 3 ] { \frac { 686 } { 2 } }$

Accepted Answer

A) 7 
B)  $7 \sqrt [ 3 ] { 2 }$ 
C)  $\sqrt [ 3 ] { 343 }$ 
D)  $\sqrt [ 3 ] { \frac { 686 } { 2 } }$ 
A) 7 
B)  $7 \sqrt [ 3 ] { 2 }$ 
C)  $\sqrt [ 3 ] { 343 }$ 
D)  $\sqrt [ 3 ] { \frac { 686 } { 2 } }$

Question 14

Multiply. Write the result in the form a + bi.
-(8 - 2i)(3 + 7i)

Accepted Answer

A)  $38 - 50 \mathrm { i }$ 
B)  $10 - 62 \mathrm { i }$ 
C)  $38 + 50 \mathrm { i }$ 
D)  $- 14 i ^ { 2 } + 50 i + 24$ 
A)  $38 - 50 \mathrm { i }$ 
B)  $10 - 62 \mathrm { i }$ 
C)  $38 + 50 \mathrm { i }$ 
D)  $- 14 i ^ { 2 } + 50 i + 24$

Question 15

Find the area of the figure in radical form with the radicals simplified.
-

Accepted Answer

A) 216 
B) 36 
C)  $6 \sqrt { 6 }$ 
D)  $36 \sqrt { 6 }$ 
A) 216 
B) 36 
C)  $6 \sqrt { 6 }$ 
D)  $36 \sqrt { 6 }$

Question 16

Simplify by rationalizing the denominator.
-$\frac { 3 \sqrt { x } + \sqrt { y } } { \sqrt { y } - 3 \sqrt { x } }$

Accepted Answer

A)  $\frac { 9 x + \sqrt { y } + 6 \sqrt { x y } } { y - 9 x }$ 
B)  $\frac { 9 x + y + 6 \sqrt { x y } } { y - 3 x }$ 
C)  $\frac { 9 \sqrt { x } + y + 6 \sqrt { x y } } { y - 9 x }$ 
D)  $\frac { 9 x + y + 6 \sqrt { x y } } { y - 9 x }$ 
A)  $\frac { 9 x + \sqrt { y } + 6 \sqrt { x y } } { y - 9 x }$ 
B)  $\frac { 9 x + y + 6 \sqrt { x y } } { y - 3 x }$ 
C)  $\frac { 9 \sqrt { x } + y + 6 \sqrt { x y } } { y - 9 x }$ 
D)  $\frac { 9 x + y + 6 \sqrt { x y } } { y - 9 x }$

Question 17

Simplify. Assume all variables represent positive real numbers.
-$\frac { 3 } { \sqrt { 5 p } }$

Accepted Answer

A)  $\frac { 3 \sqrt { 5 p } } { 5 p }$ 
B)  $3 \sqrt { 5 p }$ 
C)  $28 p$ 
D)  $\frac { 9 \sqrt { 5 p } } { 5 p }$ 
A)  $\frac { 3 \sqrt { 5 p } } { 5 p }$ 
B)  $3 \sqrt { 5 p }$ 
C)  $28 p$ 
D)  $\frac { 9 \sqrt { 5 p } } { 5 p }$

Question 18

Simplify.
-$\sqrt { \frac { 2835 x ^ { 11 } } { 5 x ^ { 9 } } }$

Accepted Answer

A)  $9 \times \sqrt { 35 }$ 
B)  $x \sqrt { 567 }$ 
C)  $9 x \sqrt { 7 }$ 
D)  $9 x ^{10}\sqrt { 7 }$ 
A)  $9 \times \sqrt { 35 }$ 
B)  $x \sqrt { 567 }$ 
C)  $9 x \sqrt { 7 }$ 
D)  $9 x ^{10}\sqrt { 7 }$

Question 19

Write as an absolute value.
-$\sqrt { w ^ { 24 } }$

Accepted Answer

A)  $\left| w ^ { 12 } \right|$ 
B)  $w ^ { 12 }$ 
C)  $w ^ { 22 }$ 
D)  $-w^{ 12}$ 
A)  $\left| w ^ { 12 } \right|$ 
B)  $w ^ { 12 }$ 
C)  $w ^ { 22 }$ 
D)  $-w^{ 12}$

Question 20

Write the expression in radical form. Assume that all variables represent positive real numbers.
-$\left( 6 x ^ { 2 } y ^ { 3 } \right) ^ { 5 / 3 }$

Accepted Answer

A)  $\left( \sqrt [ 5 ] { \frac { 6 } { 5 } x ^ { 2 } y ^ { 3 } } \right) ^ { 3 }$ 
B)  $\left( \sqrt [ 5 ] { 6 x ^ { 2 } y ^ { 3 } } \right) ^ { 3 }$ 
C)  $\left( \sqrt [ 3 ] { 6 x ^ { 2 } y ^ { 3 } } \right) ^ { 5 }$ 
D)  $\left( \sqrt [ 3 ] { 2 x ^ { 2 } y ^ { 3 } } \right) ^ { 5 }$ 
A)  $\left( \sqrt [ 5 ] { \frac { 6 } { 5 } x ^ { 2 } y ^ { 3 } } \right) ^ { 3 }$ 
B)  $\left( \sqrt [ 5 ] { 6 x ^ { 2 } y ^ { 3 } } \right) ^ { 3 }$ 
C)  $\left( \sqrt [ 3 ] { 6 x ^ { 2 } y ^ { 3 } } \right) ^ { 5 }$ 
D)  $\left( \sqrt [ 3 ] { 2 x ^ { 2 } y ^ { 3 } } \right) ^ { 5 }$

Divide. - $\frac { \sqrt { - 1000 } \sqrt { - 8 } } { \sqrt { - 25 } }$

Simplify. - $( \sqrt { 10 } + \sqrt { 2 } ) ( \sqrt { 10 } - \sqrt { 2 } )$

Simplify. - $\frac { \sqrt { 7 } } { 7 } + \frac { 2 } { \sqrt { 7 } } + \sqrt { 28 }$

Evaluate if possible. If the expression is not a real number, so state. - $27 ^ { - 1 / 3 }$

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt { 6 x - 5 } = 5$

Simplify. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { \frac { 7 } { 3 } }$

Simplify. - $5 \sqrt [ 3 ] { x ^ { 2 } } \left( \sqrt [ 3 ] { 25 x } - \sqrt [ 3 ] { 25 x ^ { 8 } } \right)$

Simplify. - $3 \sqrt [ 3 ] { 256 x } - 4 \sqrt [ 3 ] { 108 x }$

Simplify. - $\sqrt [ 3 ] { \mathrm { p } ^ { 32 } }$

Evaluate. - $\mathrm { i } ^ { 21 }$

Multiply. Write the result in the form a + bi. - $\left( \frac { 1 } { 3 } - \frac { 1 } { 2 } \mathrm { i } \right) \left( \frac { 3 } { 5 } - \frac { 3 } { 5 } \mathrm { i } \right)$

Simplify. -3 - 6 108 + 3 300

Simplify. - $\sqrt [ 3 ] { \frac { 686 } { 2 } }$

Multiply. Write the result in the form a + bi. -(8 - 2i)(3 + 7i)

Find the area of the figure in radical form with the radicals simplified. -

Simplify by rationalizing the denominator. - $\frac { 3 \sqrt { x } + \sqrt { y } } { \sqrt { y } - 3 \sqrt { x } }$

Simplify. Assume all variables represent positive real numbers. - $\frac { 3 } { \sqrt { 5 p } }$

Simplify. - $\sqrt { \frac { 2835 x ^ { 11 } } { 5 x ^ { 9 } } }$

Write as an absolute value. - $\sqrt { w ^ { 24 } }$

Write the expression in radical form. Assume that all variables represent positive real numbers. - $\left( 6 x ^ { 2 } y ^ { 3 } \right) ^ { 5 / 3 }$

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

Divide. - −1000−8−25\frac { \sqrt { - 1000 } \sqrt { - 8 } } { \sqrt { - 25 } }−25​−1000​−8​​

Simplify. - (10+2)(10−2)( \sqrt { 10 } + \sqrt { 2 } ) ( \sqrt { 10 } - \sqrt { 2 } )(10​+2​)(10​−2​)

Simplify. - 77+27+28\frac { \sqrt { 7 } } { 7 } + \frac { 2 } { \sqrt { 7 } } + \sqrt { 28 }77​​+7​2​+28​

Evaluate if possible. If the expression is not a real number, so state. - 27−1/327 ^ { - 1 / 3 }27−1/3

Solve and check your solution(s). If the equation has no real solution, so state. - 6x−5=5\sqrt { 6 x - 5 } = 56x−5​=5

Simplify. Assume all variables represent positive real numbers. - 733\sqrt [ 3 ] { \frac { 7 } { 3 } }337​​

Simplify. - 5x23(25x3−25x83)5 \sqrt [ 3 ] { x ^ { 2 } } \left( \sqrt [ 3 ] { 25 x } - \sqrt [ 3 ] { 25 x ^ { 8 } } \right)53x2​(325x​−325x8​)

Simplify. - 3256x3−4108x33 \sqrt [ 3 ] { 256 x } - 4 \sqrt [ 3 ] { 108 x }33256x​−43108x​

Simplify. - p323\sqrt [ 3 ] { \mathrm { p } ^ { 32 } }3p32​

Evaluate. - i21\mathrm { i } ^ { 21 }i21

Multiply. Write the result in the form a + bi. - (13−12i)(35−35i)\left( \frac { 1 } { 3 } - \frac { 1 } { 2 } \mathrm { i } \right) \left( \frac { 3 } { 5 } - \frac { 3 } { 5 } \mathrm { i } \right)(31​−21​i)(53​−53​i)