Question 1

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

Accepted Answer

A)  $\frac { 16 } { 3 }$ 
B)  $\frac { 20 } { 3 }$ 
C) 4 
D) 16 
A)  $\frac { 16 } { 3 }$ 
B)  $\frac { 20 } { 3 }$ 
C) 4 
D) 16

Question 2

Solve the problem.
-Scott set up a volleyball net in his backyard. One of the poles, which forms a right angle with the ground, is 7 feet high. To secure the pole, he attached a rope from the top of the pole to a stake 3 feet from the bottom of the
Pole. To the nearest tenth of a foot, find the length of the rope.

Accepted Answer

A) 58 ft 
B) 3.2 ft 
C) 6.3 ft 
D) 7.6 ft 
A) 58 ft 
B) 3.2 ft 
C) 6.3 ft 
D) 7.6 ft

Question 3

Multiply. Write the result in the form a + bi.
-$( \sqrt { 8 } + 2 \mathrm { i } ) ( \sqrt { 8 } - 2 \mathrm { i } )$

Accepted Answer

A)  $8 - 2 \mathrm { i } \sqrt { 2 }$ 
B) 4 
C) 12 
D) 8 - 4i 
A)  $8 - 2 \mathrm { i } \sqrt { 2 }$ 
B) 4 
C) 12 
D) 8 - 4i

Question 4

Simplify.
-$2 + 9 \sqrt [ 3 ] { x } - 2 \sqrt [ 3 ] { x } + 6$

Accepted Answer

A)  $7 \sqrt [ 3 ] { x } + 8$ 
B)  $18 \sqrt [ 3 ] { x } + 12$ 
C)  $18 \sqrt [ 3 ] { x } + 8$ 
D)  $11 \sqrt [ 3 ] { x } + 8$ 
A)  $7 \sqrt [ 3 ] { x } + 8$ 
B)  $18 \sqrt [ 3 ] { x } + 12$ 
C)  $18 \sqrt [ 3 ] { x } + 8$ 
D)  $11 \sqrt [ 3 ] { x } + 8$

Question 5

Simplify.
-$\sqrt { \frac { 50 } { 2 } }$

Accepted Answer

A)  $\frac { 5 } { \sqrt { 2 } }$ 
B) 2 
C) 5 
D)  $5 \sqrt { 2 }$ 
A)  $\frac { 5 } { \sqrt { 2 } }$ 
B) 2 
C) 5 
D)  $5 \sqrt { 2 }$

Question 6

Simplify by rationalizing the denominator.
-$\frac { 6 } { 8 - \sqrt { 5 } }$

Accepted Answer

A)  $\frac { 48 + 6 \sqrt { 5 } } { 59 }$ 
B)  $\frac { 48 - 6 \sqrt { 5 } } { 59 }$ 
C)  $\frac { 6 } { 8 } - \frac { 6 } { \sqrt { 5 } }$ 
D)  $\frac { 48 + 6 \sqrt { 5 } } { - 3 }$ 
A)  $\frac { 48 + 6 \sqrt { 5 } } { 59 }$ 
B)  $\frac { 48 - 6 \sqrt { 5 } } { 59 }$ 
C)  $\frac { 6 } { 8 } - \frac { 6 } { \sqrt { 5 } }$ 
D)  $\frac { 48 + 6 \sqrt { 5 } } { - 3 }$

Question 7

Simplify. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { \frac { 11 m ^ { 9 } n ^ { 8 } } { 5 p ^ { 4 } } }$

Accepted Answer

A)  $\frac { m ^ { 3 } n \sqrt [ 3 ] { 55 n ^ { 2 } p ^ { 2 } } } { p ^ { 2 } }$ 
B)  $\frac { m ^ { 3 } n ^ { 2 } \sqrt [ 3 ] { 5 n ^ { 2 } p ^ { 2 } } } { p ^ { 2 } }$ 
C)  $\frac { m n ^ { 2 } \sqrt [ 3 ] { 275 n ^ { 2 } p ^ { 2 } } } { 5 }$ 
D)  $\frac { m ^ { 3 } n ^ { 2 } \sqrt [ 3 ] { 275 n ^ { 2 } p ^ { 2 } } } { 5 p ^ { 2 } }$ 
A)  $\frac { m ^ { 3 } n \sqrt [ 3 ] { 55 n ^ { 2 } p ^ { 2 } } } { p ^ { 2 } }$ 
B)  $\frac { m ^ { 3 } n ^ { 2 } \sqrt [ 3 ] { 5 n ^ { 2 } p ^ { 2 } } } { p ^ { 2 } }$ 
C)  $\frac { m n ^ { 2 } \sqrt [ 3 ] { 275 n ^ { 2 } p ^ { 2 } } } { 5 }$ 
D)  $\frac { m ^ { 3 } n ^ { 2 } \sqrt [ 3 ] { 275 n ^ { 2 } p ^ { 2 } } } { 5 p ^ { 2 } }$

Question 8

Write the expression in radical form. Assume that all variables represent positive real numbers.
-$( 7 x + 2 ) ^ { 2 / 7 }$

Accepted Answer

A)  $\sqrt [ 7 ] { 7 x ^ { 2 } + 4 }$ 
B)  $( \sqrt [ 7 ] { ( 7 x + 2 ) } ) ^ { 2 }$ 
C)  $\sqrt [ 7 ] { 49 x ^ { 2 } + 4 }$ 
D)  $( \sqrt [ 2 ] { ( 7 x + 2 ) } ) ^ { 7 }$ 
A)  $\sqrt [ 7 ] { 7 x ^ { 2 } + 4 }$ 
B)  $( \sqrt [ 7 ] { ( 7 x + 2 ) } ) ^ { 2 }$ 
C)  $\sqrt [ 7 ] { 49 x ^ { 2 } + 4 }$ 
D)  $( \sqrt [ 2 ] { ( 7 x + 2 ) } ) ^ { 7 }$

Question 9

Solve and check your solution(s). If the equation has no real solution, so state.
-$\sqrt { y ^ { 2 } - 5 y + 4 } = y - 3$

Accepted Answer

A) -5 
B) 2 
C)  $- \frac { 5 } { 2 }$ 
D) 5 
A) -5 
B) 2 
C)  $- \frac { 5 } { 2 }$ 
D) 5

Question 10

Solve and check your solution(s). If the equation has no real solution, so state.
-$( 4 x + 5 ) ^ { 1 / 2 } = 4$

Accepted Answer

A) 4 
B) 20 
C)  $- \frac { 5 } { 4 }$ 
D)  $\frac { 11 } { 4 }$ 
A) 4 
B) 20 
C)  $- \frac { 5 } { 4 }$ 
D)  $\frac { 11 } { 4 }$

Question 11

Simplify.
-$\sqrt [ 3 ] { - 64 a ^ { 14 } b ^ { 7 } }$

Accepted Answer

A)  $4 a ^ { 2 } b \sqrt [ 3 ] { a ^ { 4 } b ^ { 2 } }$ 
B)  $- 4 a ^ { 4 } b ^ { 2 } \sqrt [ 3 ] { a ^ { 2 } b }$ 
C)  $4 \sqrt { a ^ { 7 } b ^ { 14 } }$ 
D)  $4 a b \sqrt [ 3 ] { a ^ { 3 } b ^ { 5 } }$ 
A)  $4 a ^ { 2 } b \sqrt [ 3 ] { a ^ { 4 } b ^ { 2 } }$ 
B)  $- 4 a ^ { 4 } b ^ { 2 } \sqrt [ 3 ] { a ^ { 2 } b }$ 
C)  $4 \sqrt { a ^ { 7 } b ^ { 14 } }$ 
D)  $4 a b \sqrt [ 3 ] { a ^ { 3 } b ^ { 5 } }$

Question 12

Write the expression in exponential form. Assume that all variables represent positive real numbers.
-$\sqrt [ 9 ] { 5 ^ { 11 } }$

Accepted Answer

A)  $5 ^ { 11 / 2 }$ 
B)  $5 ^ { 9 }$ 
C)  $5 ^ { 2 / 11 }$ 
D)  $5 ^ { - 11 / 2 }$ 
A)  $5 ^ { 11 / 2 }$ 
B)  $5 ^ { 9 }$ 
C)  $5 ^ { 2 / 11 }$ 
D)  $5 ^ { - 11 / 2 }$

Question 13

Simplify. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { \frac { 7 } { 9 x ^ { 2 } } }$

Accepted Answer

A)  $\frac { \sqrt [ 3 ] { 567 x } } { 81 }$ 
B)  $\frac { \sqrt [ 3 ] { 63 x } } { 9 x }$ 
C)  $\frac { \sqrt [ 3 ] { 567 x ^ { 2 } } } { 9 x }$ 
D)  $\frac { \sqrt [ 3 ] { 21 x } } { 3 x }$ 
A)  $\frac { \sqrt [ 3 ] { 567 x } } { 81 }$ 
B)  $\frac { \sqrt [ 3 ] { 63 x } } { 9 x }$ 
C)  $\frac { \sqrt [ 3 ] { 567 x ^ { 2 } } } { 9 x }$ 
D)  $\frac { \sqrt [ 3 ] { 21 x } } { 3 x }$

Question 14

Simplify by rationalizing the denominator.
-$\frac { \sqrt { x } - 20 } { \sqrt { x } + \sqrt { 6 } }$

Accepted Answer

A)  $\frac { \sqrt { 6 x } + 20 \sqrt { x } - 20 \sqrt { 6 } } { 6 }$ 
B)  $\frac { x - \sqrt { 6 x } - 20 \sqrt { x } + 20 \sqrt { 6 } } { x - 6 }$ 
C)  $\frac { x - 26 \sqrt { x } + 20 \sqrt { 6 } } { x - 6 }$ 
D)  $\frac { - 20 \sqrt { 6 } } { 6 }$ 
A)  $\frac { \sqrt { 6 x } + 20 \sqrt { x } - 20 \sqrt { 6 } } { 6 }$ 
B)  $\frac { x - \sqrt { 6 x } - 20 \sqrt { x } + 20 \sqrt { 6 } } { x - 6 }$ 
C)  $\frac { x - 26 \sqrt { x } + 20 \sqrt { 6 } } { x - 6 }$ 
D)  $\frac { - 20 \sqrt { 6 } } { 6 }$

Question 15

Multiply. Write the result in the form a + bi.
-$( 6 - 6 i ) ( 2 + 7 i )$

Accepted Answer

A)  $- 42 i ^ { 2 } + 30 i + 12$ 
B)  $54 + 30 \mathrm { i }$ 
C)  $- 30 - 54 i$ 
D)  $54 - 30 \mathrm { i }$ 
A)  $- 42 i ^ { 2 } + 30 i + 12$ 
B)  $54 + 30 \mathrm { i }$ 
C)  $- 30 - 54 i$ 
D)  $54 - 30 \mathrm { i }$

Question 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.
-$$\sqrt [ 4 ] { 104 }$$

Accepted Answer

A) 3.2 
B) 26 
C) 3.19 
D) not a real number 
A) 3.2 
B) 26 
C) 3.19 
D) not a real number

Question 17

Solve. You will have to square both sides of the equation twice to eliminate all radicals.
-$\sqrt { 2 x + 5 } = 3 + \sqrt { x - 2 }$

Accepted Answer

A) -38, -2 
B) -2, 38 
C) 2, 38 
D) no real solution 
A) -38, -2 
B) -2, 38 
C) 2, 38 
D) no real solution

Question 18

Simplify.
-$4 \sqrt [ 3 ] { 64 x } + 4 \sqrt [ 3 ] { 8 x }$

Accepted Answer

A)  $24 \sqrt [ 3 ] { x }$ 
B)  $6 \sqrt [ 3 ] { x }$ 
C) 24x 
D)  $4 \sqrt [ 3 ] { 72 x }$ 
A)  $24 \sqrt [ 3 ] { x }$ 
B)  $6 \sqrt [ 3 ] { x }$ 
C) 24x 
D)  $4 \sqrt [ 3 ] { 72 x }$

Question 19

Simplify.
-7 48 - 9 192 - 7 147

Accepted Answer

A) -14 3 
B) -93 3 
C) 7 3 
D) 14 3 
A) -14 3 
B) -93 3 
C) 7 3 
D) 14 3

Question 20

Simplify.
-$4 \sqrt [ 3 ] { x ^ { 2 } y ^ { 5 } } \left( \sqrt [ 3 ] { 64 x ^ { 9 } y ^ { 5 } } + \sqrt [ 3 ] { 256 x y ^ { 9 } } \right)$

Accepted Answer

A)  $16 x y ^ { 3 } \sqrt [ 3 ] { x ^ { 2 } y } + 16 y ^ { 4 } \sqrt [ 3 ] { 4 y ^ { 2 } }$ 
B)  $4 x ^ { 3 } y ^ { 3 } \sqrt [ 3 ] { x ^ { 2 } y } + 16 x y ^ { 3 } \sqrt [ 3 ] { 4 y ^ { 2 } }$ 
C)  $16 x ^ { 3 } y ^ { 3 } \sqrt [ 3 ] { x ^ { 2 } } + 16 x y ^ { 4 } \sqrt [ 3 ] { y ^ { 2 } }$ 
D)  $16 x ^ { 3 } y ^ { 3 } \sqrt [ 3 ] { x ^ { 2 } y } + 16 x y ^ { 4 } \sqrt [ 3 ] { 4 y ^ { 2 } }$ 
A)  $16 x y ^ { 3 } \sqrt [ 3 ] { x ^ { 2 } y } + 16 y ^ { 4 } \sqrt [ 3 ] { 4 y ^ { 2 } }$ 
B)  $4 x ^ { 3 } y ^ { 3 } \sqrt [ 3 ] { x ^ { 2 } y } + 16 x y ^ { 3 } \sqrt [ 3 ] { 4 y ^ { 2 } }$ 
C)  $16 x ^ { 3 } y ^ { 3 } \sqrt [ 3 ] { x ^ { 2 } } + 16 x y ^ { 4 } \sqrt [ 3 ] { y ^ { 2 } }$ 
D)  $16 x ^ { 3 } y ^ { 3 } \sqrt [ 3 ] { x ^ { 2 } y } + 16 x y ^ { 4 } \sqrt [ 3 ] { 4 y ^ { 2 } }$

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

Multiply. Write the result in the form a + bi. - $( \sqrt { 8 } + 2 \mathrm { i } ) ( \sqrt { 8 } - 2 \mathrm { i } )$

Simplify. - $2 + 9 \sqrt [ 3 ] { x } - 2 \sqrt [ 3 ] { x } + 6$

Simplify. - $\sqrt { \frac { 50 } { 2 } }$

Simplify by rationalizing the denominator. - $\frac { 6 } { 8 - \sqrt { 5 } }$

Simplify. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { \frac { 11 m ^ { 9 } n ^ { 8 } } { 5 p ^ { 4 } } }$

Write the expression in radical form. Assume that all variables represent positive real numbers. - $( 7 x + 2 ) ^ { 2 / 7 }$

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt { y ^ { 2 } - 5 y + 4 } = y - 3$

Solve and check your solution(s). If the equation has no real solution, so state. - $( 4 x + 5 ) ^ { 1 / 2 } = 4$

Simplify. - $\sqrt [ 3 ] { - 64 a ^ { 14 } b ^ { 7 } }$

Write the expression in exponential form. Assume that all variables represent positive real numbers. - $\sqrt [ 9 ] { 5 ^ { 11 } }$

Simplify. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { \frac { 7 } { 9 x ^ { 2 } } }$

Simplify by rationalizing the denominator. - $\frac { \sqrt { x } - 20 } { \sqrt { x } + \sqrt { 6 } }$

Multiply. Write the result in the form a + bi. - $( 6 - 6 i ) ( 2 + 7 i )$

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. - $\sqrt [ 4 ] { 104 }$

Solve. You will have to square both sides of the equation twice to eliminate all radicals. - $\sqrt { 2 x + 5 } = 3 + \sqrt { x - 2 }$

Simplify. - $4 \sqrt [ 3 ] { 64 x } + 4 \sqrt [ 3 ] { 8 x }$

Simplify. -7 48 - 9 192 - 7 147

Simplify. - $4 \sqrt [ 3 ] { x ^ { 2 } y ^ { 5 } } \left( \sqrt [ 3 ] { 64 x ^ { 9 } y ^ { 5 } } + \sqrt [ 3 ] { 256 x y ^ { 9 } } \right)$

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

Solve and check your solution(s). If the equation has no real solution, so state. - 3y+4=4\sqrt { 3 y + 4 } = 43y+4​=4

Multiply. Write the result in the form a + bi. - (8+2i)(8−2i)( \sqrt { 8 } + 2 \mathrm { i } ) ( \sqrt { 8 } - 2 \mathrm { i } )(8​+2i)(8​−2i)

Simplify. - 2+9x3−2x3+62 + 9 \sqrt [ 3 ] { x } - 2 \sqrt [ 3 ] { x } + 62+93x​−23x​+6

Simplify. - 502\sqrt { \frac { 50 } { 2 } }250​​

Simplify by rationalizing the denominator. - 68−5\frac { 6 } { 8 - \sqrt { 5 } }8−5​6​

Simplify. Assume all variables represent positive real numbers. - 11m9n85p43\sqrt [ 3 ] { \frac { 11 m ^ { 9 } n ^ { 8 } } { 5 p ^ { 4 } } }35p411m9n8​​

Write the expression in radical form. Assume that all variables represent positive real numbers. - (7x+2)2/7( 7 x + 2 ) ^ { 2 / 7 }(7x+2)2/7

Solve and check your solution(s). If the equation has no real solution, so state. - y2−5y+4=y−3\sqrt { y ^ { 2 } - 5 y + 4 } = y - 3y2−5y+4​=y−3

Solve and check your solution(s). If the equation has no real solution, so state. - (4x+5)1/2=4( 4 x + 5 ) ^ { 1 / 2 } = 4(4x+5)1/2=4

Simplify. - −64a14b73\sqrt [ 3 ] { - 64 a ^ { 14 } b ^ { 7 } }3−64a14b7​

Write the expression in exponential form. Assume that all variables represent positive real numbers. - 5119\sqrt [ 9 ] { 5 ^ { 11 } }9511​

Simplify. Assume all variables represent positive real numbers. - 79x23\sqrt [ 3 ] { \frac { 7 } { 9 x ^ { 2 } } }39x27​​

Simplify by rationalizing the denominator. - x−20x+6\frac { \sqrt { x } - 20 } { \sqrt { x } + \sqrt { 6 } }x​+6​x​−20​

Multiply. Write the result in the form a + bi. - (6−6i)(2+7i)( 6 - 6 i ) ( 2 + 7 i )(6−6i)(2+7i)

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. - 1044\sqrt [ 4 ] { 104 }4104​

Solve. You will have to square both sides of the equation twice to eliminate all radicals. - 2x+5=3+x−2\sqrt { 2 x + 5 } = 3 + \sqrt { x - 2 }2x+5​=3+x−2​

Simplify. - 464x3+48x34 \sqrt [ 3 ] { 64 x } + 4 \sqrt [ 3 ] { 8 x }4364x​+438x​