Question 1

Solve. You will have to square both sides of the equation twice to eliminate all radicals.
-$\sqrt { x + 6 } + \sqrt { 2 - x } = 4$

Accepted Answer

A) 2, -2 
B) 0 
C) -2 
D) no real solution 
A) 2, -2 
B) 0 
C) -2 
D) no real solution

Question 2

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

Accepted Answer

A) 68 
B) -60 
C)  $4 - 64 \mathrm { i } ^ { 2 }$ 
D)  $4 - 64 i$ 
A) 68 
B) -60 
C)  $4 - 64 \mathrm { i } ^ { 2 }$ 
D)  $4 - 64 i$

Question 3

Simplify.
-$\sqrt [ 3 ] { \frac { x ^ { 12 } } { 27 y ^ { 6 } } }$

Accepted Answer

A)  $\frac { x ^ { 4 } } { 9 y ^ { 2 } }$ 
B)  $\frac { x ^ { 3 } } { 3 y ^ { 3 } }$ 
C)  $\frac { 3 y ^ { 2 } } { x ^ { 4 } }$ 
D)  $\frac { x ^ { 4 } } { 3 y ^ { 2 } }$ 
A)  $\frac { x ^ { 4 } } { 9 y ^ { 2 } }$ 
B)  $\frac { x ^ { 3 } } { 3 y ^ { 3 } }$ 
C)  $\frac { 3 y ^ { 2 } } { x ^ { 4 } }$ 
D)  $\frac { x ^ { 4 } } { 3 y ^ { 2 } }$

Question 4

Simplify.
-$\sqrt [ 3 ] { 162 }$

Accepted Answer

A)  $3 \sqrt [ 3 ] { 6 }$ 
B) 18 
C) 3 
D)  $3 \sqrt [ 3 ] { 18 }$ 
A)  $3 \sqrt [ 3 ] { 6 }$ 
B) 18 
C) 3 
D)  $3 \sqrt [ 3 ] { 18 }$

Question 5

Simplify. Assume all variables represent positive real numbers.
-$\frac { 15 } { \sqrt { 15 } }$

Accepted Answer

A)  $15 \sqrt { 15 }$ 
B) 15 
C)  $\sqrt { 15 }$ 
D) 1 
A)  $15 \sqrt { 15 }$ 
B) 15 
C)  $\sqrt { 15 }$ 
D) 1

Question 6

Write the expression in radical form. Assume that all variables represent positive real numbers.
-$x ^ { 1 / 5 }$

Accepted Answer

A)  $\sqrt { 5 x }$ 
B)  $- \sqrt [ 6 ] { x }$ 
C)  $\sqrt [ 6 ] { x }$ 
D)  $\sqrt [ 6 ] { \frac { 1 } { x } }$ 
A)  $\sqrt { 5 x }$ 
B)  $- \sqrt [ 6 ] { x }$ 
C)  $\sqrt [ 6 ] { x }$ 
D)  $\sqrt [ 6 ] { \frac { 1 } { x } }$

Question 7

Divide.
-$\frac { 8 - 7 i } { 5 - 3 i }$

Accepted Answer

A)  $\frac { 61 } { 34 } - \frac { 11 } { 34 } \mathrm { i }$ 
B)  $\frac { 19 } { 34 } + \frac { 59 } { 34 } \mathrm { i }$ 
C)  $\frac { 61 } { 16 } - \frac { 11 } { 16 } i$ 
D)  $\frac { 19 } { 16 } - \frac { 11 } { 16 } \mathrm { i }$ 
A)  $\frac { 61 } { 34 } - \frac { 11 } { 34 } \mathrm { i }$ 
B)  $\frac { 19 } { 34 } + \frac { 59 } { 34 } \mathrm { i }$ 
C)  $\frac { 61 } { 16 } - \frac { 11 } { 16 } i$ 
D)  $\frac { 19 } { 16 } - \frac { 11 } { 16 } \mathrm { i }$

Question 8

Write the expression in exponential form. Assume that all variables represent positive real numbers.
-$( \sqrt { x } ) ^ { 11 }$

Accepted Answer

A)  $x ^ { 11 / 5 }$ 
B)  $x ^ { 6 }$ 
C) x5/11 
D)  $x ^ { - 11 / 5 }$ 
A)  $x ^ { 11 / 5 }$ 
B)  $x ^ { 6 }$ 
C) x5/11 
D)  $x ^ { - 11 / 5 }$

Question 9

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

Accepted Answer

A) -3, 1 
B) 3, -1 
C) 3 
D) no real solution 
A) -3, 1 
B) 3, -1 
C) 3 
D) no real solution

Question 10

Simplify.
-9 7 + 3 28

Accepted Answer

A) 12 7 
B) -3 7 
C) -15 7 
D) 15 7 
A) 12 7 
B) -3 7 
C) -15 7 
D) 15 7

Question 11

Solve the problem.
-The radius of a spherical balloon is found usingdius of a spherical balloon is found using r $r = \sqrt { \frac { S } { 4 \pi } }$ where S i where S s the surface area of the balloon. Approximate the radius of a balloon whose surface area is 18 square inches. (Round to the nearest hundredth.)

Accepted Answer

A) 0.28 in. 
B) 2.39 in. 
C) 1.20 in. 
D) 2.12 in. 
A) 0.28 in. 
B) 2.39 in. 
C) 1.20 in. 
D) 2.12 in.

Question 12

Simplify.
-$\frac { \sqrt { 448 x ^ { 5 } y ^ { 6 } } } { \sqrt { 2 x y } }$

Accepted Answer

A)  $4 x ^ { 2 } y ^ { 2 } \sqrt { 14 y }$ 
B)  $4 x ^ { 2 } y ^ { 2 } \sqrt { 2 y }$ 
C)  $56 x ^ { 2 } y ^ { 2 } \sqrt { y }$ 
D)  $4 x ^ { 2 } y ^ { 2 } \sqrt { 14 }$ 
A)  $4 x ^ { 2 } y ^ { 2 } \sqrt { 14 y }$ 
B)  $4 x ^ { 2 } y ^ { 2 } \sqrt { 2 y }$ 
C)  $56 x ^ { 2 } y ^ { 2 } \sqrt { y }$ 
D)  $4 x ^ { 2 } y ^ { 2 } \sqrt { 14 }$

Question 13

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.
-$\sqrt { - 16 }$

Accepted Answer

A) 4 
B) 256 
C) -4 
D) not a real number 
A) 4 
B) 256 
C) -4 
D) not a real number

Question 14

Multiply.
-$2 x ^ { - 1 / 2 } \left( 3 x ^ { 5 } - x ^ { 1 / 2 } \right)$

Accepted Answer

A)  $6 x ^ { 9 / 2 } - 2$ 
B)  $6 x ^ { 9 / 2 } - 1$ 
C)  $6 x ^ { 9 / 2 } - x$ 
D)  $6 x ^ { 9 / 2 } - 2 x$ 
A)  $6 x ^ { 9 / 2 } - 2$ 
B)  $6 x ^ { 9 / 2 } - 1$ 
C)  $6 x ^ { 9 / 2 } - x$ 
D)  $6 x ^ { 9 / 2 } - 2 x$

Question 15

Simplify.
-6x2 - 4 54x2 - 7 54x2

Accepted Answer

A) -11x 28 
B) -11x 6 
C) -32x 6 
D) -32x 28 
A) -11x 28 
B) -11x 6 
C) -32x 6 
D) -32x 28

Question 16

Factor. Write the answer without negative exponents.
-x $x ^ { 8 / 7 } + x ^ { - 6 / 7 }$

Accepted Answer

A)  $\frac { x ^ { 2 } + x } { x ^ { 6 / 7 } }$ 
B)  $\frac { ( x + 1 ) ( x + 1 ) } { x ^ { 6 / 7 } }$ 
C)  $\frac { x ^ { 2 } + 1 } { x ^ { 6 / 7 } }$ 
D)  $\frac { ( x + 1 ) ( x - 1 ) } { x ^ { 6 / 7 } }$ 
A)  $\frac { x ^ { 2 } + x } { x ^ { 6 / 7 } }$ 
B)  $\frac { ( x + 1 ) ( x + 1 ) } { x ^ { 6 / 7 } }$ 
C)  $\frac { x ^ { 2 } + 1 } { x ^ { 6 / 7 } }$ 
D)  $\frac { ( x + 1 ) ( x - 1 ) } { x ^ { 6 / 7 } }$

Question 17

Simplify by rationalizing the denominator.
-$\frac { 5 } { \sqrt { 10 } + \sqrt { 15 } }$

Accepted Answer

A)  $\sqrt { 15 } + \sqrt { 10 }$ 
B)  $\sqrt { 5 }$ 
C)  $\sqrt { 15 } - \sqrt { 10 }$ 
D)  $\sqrt { 10 } - \sqrt { 15 }$ 
A)  $\sqrt { 15 } + \sqrt { 10 }$ 
B)  $\sqrt { 5 }$ 
C)  $\sqrt { 15 } - \sqrt { 10 }$ 
D)  $\sqrt { 10 } - \sqrt { 15 }$

Question 18

Simplify. Assume all variables represent positive real numbers.
-$\frac { 7 } { \sqrt [ 4 ] { a ^ { 3 } } }$

Accepted Answer

A)  $\frac { 7 \sqrt [ 4 ] { a ^ { 3 } } } { a }$ 
B)  $\frac { 7 \sqrt [ 4 ] { \mathrm { a } } } { \mathrm { a } }$ 
C)  $7 \sqrt [ 4 ] { \mathrm { a } }$ 
D)  $\frac { 7 \sqrt [ 4 ] { \mathrm { a } ^ { 2 } } } { \mathrm { a } }$ 
A)  $\frac { 7 \sqrt [ 4 ] { a ^ { 3 } } } { a }$ 
B)  $\frac { 7 \sqrt [ 4 ] { \mathrm { a } } } { \mathrm { a } }$ 
C)  $7 \sqrt [ 4 ] { \mathrm { a } }$ 
D)  $\frac { 7 \sqrt [ 4 ] { \mathrm { a } ^ { 2 } } } { \mathrm { a } }$

Question 19

Divide.
-$\frac { 1 + i } { - 1 - i }$

Accepted Answer

A) 1 
B) - i 
C) 0 
D) -1 
A) 1 
B) - i 
C) 0 
D) -1

Question 20

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

Accepted Answer

A)  $14 \sqrt { 3 } \text { in. }$ 
B)  $15 \sqrt { 3 } \text { in. }$ 
C) 864 in. 
D)  $( 9 \sqrt { 3 } + 3 \sqrt { 12 } ) \text { in. }$ 
A)  $14 \sqrt { 3 } \text { in. }$ 
B)  $15 \sqrt { 3 } \text { in. }$ 
C) 864 in. 
D)  $( 9 \sqrt { 3 } + 3 \sqrt { 12 } ) \text { in. }$

Solve. You will have to square both sides of the equation twice to eliminate all radicals. - $\sqrt { x + 6 } + \sqrt { 2 - x } = 4$

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

Simplify. - $\sqrt [ 3 ] { \frac { x ^ { 12 } } { 27 y ^ { 6 } } }$

Simplify. - $\sqrt [ 3 ] { 162 }$

Simplify. Assume all variables represent positive real numbers. - $\frac { 15 } { \sqrt { 15 } }$

Write the expression in radical form. Assume that all variables represent positive real numbers. - $x ^ { 1 / 5 }$

Divide. - $\frac { 8 - 7 i } { 5 - 3 i }$

Write the expression in exponential form. Assume that all variables represent positive real numbers. - $( \sqrt { x } ) ^ { 11 }$

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

Simplify. -9 7 + 3 28

Simplify. - $\frac { \sqrt { 448 x ^ { 5 } y ^ { 6 } } } { \sqrt { 2 x y } }$

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. - $\sqrt { - 16 }$

Multiply. - $2 x ^ { - 1 / 2 } \left( 3 x ^ { 5 } - x ^ { 1 / 2 } \right)$

Simplify. -6x2 - 4 54x2 - 7 54x2

Factor. Write the answer without negative exponents. -x $x ^ { 8 / 7 } + x ^ { - 6 / 7 }$

Simplify by rationalizing the denominator. - $\frac { 5 } { \sqrt { 10 } + \sqrt { 15 } }$

Simplify. Assume all variables represent positive real numbers. - $\frac { 7 } { \sqrt [ 4 ] { a ^ { 3 } } }$

Divide. - $\frac { 1 + i } { - 1 - i }$

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

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

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Characteristics of Functions and Their Graphs

Conic Sections

Sequences, Series, and Probability

Filters

Exam 7: Roots, Radicals, and Complex Numbers

Solve. You will have to square both sides of the equation twice to eliminate all radicals. - x+6+2−x=4\sqrt { x + 6 } + \sqrt { 2 - x } = 4x+6​+2−x​=4

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

Simplify. - x1227y63\sqrt [ 3 ] { \frac { x ^ { 12 } } { 27 y ^ { 6 } } }327y6x12​​

Simplify. - 1623\sqrt [ 3 ] { 162 }3162​

Simplify. Assume all variables represent positive real numbers. - 1515\frac { 15 } { \sqrt { 15 } }15​15​

Write the expression in radical form. Assume that all variables represent positive real numbers. - x1/5x ^ { 1 / 5 }x1/5

Divide. - 8−7i5−3i\frac { 8 - 7 i } { 5 - 3 i }5−3i8−7i​

Write the expression in exponential form. Assume that all variables represent positive real numbers. - (x)11( \sqrt { x } ) ^ { 11 }(x​)11

Solve and check your solution(s). If the equation has no real solution, so state. - x2+2=2x+5\sqrt { x ^ { 2 } + 2 } = \sqrt { 2 x + 5 }x2+2​=2x+5​