Question 1

Simplify.
-$\sqrt [ 3 ] { 5 } \sqrt [ 3 ] { 25 }$

Accepted Answer

A)  $5 \sqrt [ 3 ] { 5 }$ 
B) 25 
C) 5 
D) 125 
A)  $5 \sqrt [ 3 ] { 5 }$ 
B) 25 
C) 5 
D) 125

Question 2

Evaluate if possible. If the expression is not a real number, so state.
-$\left( 27 ^ { - 1 / 3 } \right) ^ { 0 }$

Accepted Answer

A)  $\frac { 1 } { 3 }$ 
B) 3 
C) 1 
D) not a real number 
A)  $\frac { 1 } { 3 }$ 
B) 3 
C) 1 
D) not a real number

Question 3

Simplify.
-$\frac { 1 } { \sqrt { 3 } } + \frac { \sqrt { 3 } } { 3 }$

Accepted Answer

A) 1 
B)  $\frac { \sqrt { 6 } } { 9 }$ 
C)  $\frac { 2 \sqrt { 3 } } { 3 }$ 
D)  $\frac { 3 } { 6 }$ 
A) 1 
B)  $\frac { \sqrt { 6 } } { 9 }$ 
C)  $\frac { 2 \sqrt { 3 } } { 3 }$ 
D)  $\frac { 3 } { 6 }$

Question 4

Factor. Write the answer without negative exponents.
-$y ^ { 1 / 5 } - y ^ { 11 / 5 }$

Accepted Answer

A)  $y ^ { 1 / 5 } ( y - 1 ) ( y + 1 )$ 
B)  $y ^ { 1 / 5 } ( 1 - y ) ( 1 + y )$ 
C)  $y ^ { 1 / 5 } \left( 1 - y ^ { 9 / 5 } \right)$ 
D)  $y ^ { 1 / 5 } ( 1 - 2 y )$ 
A)  $y ^ { 1 / 5 } ( y - 1 ) ( y + 1 )$ 
B)  $y ^ { 1 / 5 } ( 1 - y ) ( 1 + y )$ 
C)  $y ^ { 1 / 5 } \left( 1 - y ^ { 9 / 5 } \right)$ 
D)  $y ^ { 1 / 5 } ( 1 - 2 y )$

Question 5

Write the expression in exponential form. Assume that all variables represent positive real numbers.
-$\sqrt [ 9 ] { 4 x ^ { 12 } y ^ { 11 } }$

Accepted Answer

A)  $\left( 4 x ^ { 12 } y ^ { 11 } \right) ^ { 1 / 5 }$ 
B)  $\left( 4 x ^ { 12 } y ^ { 11 } \right) ^ { 5 }$ 
C)  $\left( \frac { 4 } { 5 } x ^ { 12 } y ^ { 11 } \right) ^ { 5 }$ 
D)  $\left( \frac { 4 } { 5 } x ^ { 12 } y ^ { 11 } \right) ^ { 1 / 5 }$ 
A)  $\left( 4 x ^ { 12 } y ^ { 11 } \right) ^ { 1 / 5 }$ 
B)  $\left( 4 x ^ { 12 } y ^ { 11 } \right) ^ { 5 }$ 
C)  $\left( \frac { 4 } { 5 } x ^ { 12 } y ^ { 11 } \right) ^ { 5 }$ 
D)  $\left( \frac { 4 } { 5 } x ^ { 12 } y ^ { 11 } \right) ^ { 1 / 5 }$

Question 6

Simplify. Write the answer in exponential form without negative exponents.
-$x ^ { - 9 / 2 }$

Accepted Answer

A)  $- x ^ { 9 / 2 }$ 
B)  $\frac { - 1 } { x ^ { 9 / 2 } }$ 
C)  $\frac { 1 } { \mathrm { x } ^ { 2 / 9 } }$ 
D)  $\frac { 1 } { x ^ { 9 / 2 } }$ 
A)  $- x ^ { 9 / 2 }$ 
B)  $\frac { - 1 } { x ^ { 9 / 2 } }$ 
C)  $\frac { 1 } { \mathrm { x } ^ { 2 / 9 } }$ 
D)  $\frac { 1 } { x ^ { 9 / 2 } }$

Question 7

Simplify.
-$\sqrt { 14 x } \sqrt { 98 x }$

Accepted Answer

A)  $14 \sqrt { 7 x ^ { 2 } }$ 
B)  $14 x ^ { 2 } \sqrt { 7 }$ 
C)  $14 \times \sqrt { 7 }$ 
D)  $14 \sqrt { 7 x }$ 
A)  $14 \sqrt { 7 x ^ { 2 } }$ 
B)  $14 x ^ { 2 } \sqrt { 7 }$ 
C)  $14 \times \sqrt { 7 }$ 
D)  $14 \sqrt { 7 x }$

Question 8

Simplify.
-7 50 + 3 8

Accepted Answer

A) 41 2 
B) -29 2 
C) 29 2 
D) -41 2 
A) 41 2 
B) -29 2 
C) 29 2 
D) -41 2

Question 9

Solve and check your solution(s). If the equation has no real solution, so state.
-$( 5 x + 4 ) ^ { 1 / 3 } = 5$

Accepted Answer

A) 25 
B)  $\frac { 21 } { 5 }$ 
C)  $\frac { 121 } { 5 }$ 
D) 30 
A) 25 
B)  $\frac { 21 } { 5 }$ 
C)  $\frac { 121 } { 5 }$ 
D) 30

Question 10

Simplify. Write the answer in exponential form without negative exponents.
-$14 x ^ { 2 / 7 } \cdot 2 x ^ { - 9 / 4 }$

Accepted Answer

A)  $\frac { 7 } { x ^ { 55 / 28 } }$ 
B)  $\frac { 28 } { x ^ { 55 / 28 } }$ 
C)  $- 28 x ^ { 55 / 28 }$ 
D)  $\frac { 1 } { 28 x ^ { 55 / 28 } }$ 
A)  $\frac { 7 } { x ^ { 55 / 28 } }$ 
B)  $\frac { 28 } { x ^ { 55 / 28 } }$ 
C)  $- 28 x ^ { 55 / 28 }$ 
D)  $\frac { 1 } { 28 x ^ { 55 / 28 } }$

Question 11

Simplify.
-$\sqrt [ 3 ] { 7 } \sqrt [ 3 ] { 147 }$

Accepted Answer

A)  $3 \sqrt [ 3 ] { 7 }$ 
B)  $$9 \sqrt [ 3 ] { 7 }$$ 
C)  $7 \sqrt [ 3 ] { 3 }$ 
D)  $21 \sqrt [ 3 ] { 3 }$ 
A)  $3 \sqrt [ 3 ] { 7 }$ 
B)  $$9 \sqrt [ 3 ] { 7 }$$ 
C)  $7 \sqrt [ 3 ] { 3 }$ 
D)  $21 \sqrt [ 3 ] { 3 }$

Question 12

Solve the problem.
-A formula for the length of a diagonal from the upper corner of a box to the opposite lower corner is $\mathrm { d } = \sqrt { \mathrm { L } ^ { 2 } + \mathrm { W } ^ { 2 } + \mathrm { H } ^ { 2 } } ,$ where L, W, and H are the length, width, and height, respectively. Find the length of t where L, W, and H are the length, width, and height, respectively. Find the length of the diagonal of the box if the length is 22 inches, width is 15 inches, and height is 6 inches. Leave your answer in
Simplified radical form.

Accepted Answer

A)  $\sqrt { 86 } \mathrm { ~in. }$ 
B)  $\sqrt { 43 } \text { in. }$ 
C)  $\sqrt { 745 } \text { in. }$ 
D)  $\sqrt { 1490 } \text { in. }$ 
A)  $\sqrt { 86 } \mathrm { ~in. }$ 
B)  $\sqrt { 43 } \text { in. }$ 
C)  $\sqrt { 745 } \text { in. }$ 
D)  $\sqrt { 1490 } \text { in. }$

Question 13

Simplify.
-$\sqrt [ 3 ] { \frac { 9 x ^ { 3 } y ^ { 11 } } { 3 x ^ { 9 } y ^ { 3 } } }$

Accepted Answer

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

Question 14

Simplify.
-$\frac { \sqrt { 75 } } { \sqrt { 3 } }$

Accepted Answer

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

Question 15

Solve the problem.
-A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so that the rope is taut while the balloon is directly above a flag pole that is 70 feet from where the rope is staked down. Find the
Altitude of the balloon if the rope is 120 feet long.

Accepted Answer

A)  $5 \sqrt { 2 } \mathrm { ft }$ 
B)  $5 \sqrt { 38 } \mathrm { ft }$ 
C)  $10 \sqrt { 193 } \mathrm { ft }$ 
D)  $10 \sqrt { 95 } \mathrm { ft }$ 
A)  $5 \sqrt { 2 } \mathrm { ft }$ 
B)  $5 \sqrt { 38 } \mathrm { ft }$ 
C)  $10 \sqrt { 193 } \mathrm { ft }$ 
D)  $10 \sqrt { 95 } \mathrm { ft }$

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.
-$$\sqrt [ 4 ] { \frac { 1 } { 625 } }$$

Accepted Answer

A)  $\frac { 1 } { 100 }$ 
B)  $\frac { 1 } { 20 }$ 
C)  $\frac { 1 } { 5 }$ 
D) not a real number 
A)  $\frac { 1 } { 100 }$ 
B)  $\frac { 1 } { 20 }$ 
C)  $\frac { 1 } { 5 }$ 
D) not a real number

Question 17

Simplify. Write the answer in exponential form without negative exponents.
-$\left( \frac { 4 ^ { 3 } x ^ { 1 / 4 } y ^ { 5 } } { x ^ { 1 / 4 } } \right) ^ { 1 / 3 }$

Accepted Answer

A)  $4 y ^ { 5 }$ 
B)  $4 y ^ { 3 / 5 }$ 
C)  $4 y ^ { 5 / 3 }$ D
D)  $y ^ { 5 / 3 }$ 
A)  $4 y ^ { 5 }$ 
B)  $4 y ^ { 3 / 5 }$ 
C)  $4 y ^ { 5 / 3 }$ D
D)  $y ^ { 5 / 3 }$

Question 18

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

Accepted Answer

A) 2, -1 
B) 2 
C) -1 
D) no real solution 
A) 2, -1 
B) 2 
C) -1 
D) no real solution

Question 19

Write as an absolute value.
-$$\sqrt { \left( 11 x ^ { 6 } - 7 y ^ { 4 } \right) ^ { 2 } }$$

Accepted Answer

A)  $\left| 11 x ^ { 6 } - 7 y ^ { 4 } \right|$ 
B)  $11 x ^ { 6 } - 7 y ^ { 4 }$ 
C)  $11 x ^ { 3 } - 7 y ^ { 2 }$ 
D)  $\left| 11 x ^ { 3 } - 7 y ^ { 2 } \right|$ 
A)  $\left| 11 x ^ { 6 } - 7 y ^ { 4 } \right|$ 
B)  $11 x ^ { 6 } - 7 y ^ { 4 }$ 
C)  $11 x ^ { 3 } - 7 y ^ { 2 }$ 
D)  $\left| 11 x ^ { 3 } - 7 y ^ { 2 } \right|$

Question 20

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.
-$$\sqrt [ 5 ] { \frac { 243 } { 32 } }$$

Accepted Answer

A)  $\frac { 27 } { 8 }$ 
B)  $\frac { 81 } { 16 }$ 
C)  $\frac { 3 } { 2 }$ 
D) not a real number 
A)  $\frac { 27 } { 8 }$ 
B)  $\frac { 81 } { 16 }$ 
C)  $\frac { 3 } { 2 }$ 
D) not a real number

Simplify. - $\sqrt [ 3 ] { 5 } \sqrt [ 3 ] { 25 }$

Evaluate if possible. If the expression is not a real number, so state. - $\left( 27 ^ { - 1 / 3 } \right) ^ { 0 }$

Simplify. - $\frac { 1 } { \sqrt { 3 } } + \frac { \sqrt { 3 } } { 3 }$

Factor. Write the answer without negative exponents. - $y ^ { 1 / 5 } - y ^ { 11 / 5 }$

Write the expression in exponential form. Assume that all variables represent positive real numbers. - $\sqrt [ 9 ] { 4 x ^ { 12 } y ^ { 11 } }$

Simplify. Write the answer in exponential form without negative exponents. - $x ^ { - 9 / 2 }$

Simplify. - $\sqrt { 14 x } \sqrt { 98 x }$

Simplify. -7 50 + 3 8

Solve and check your solution(s). If the equation has no real solution, so state. - $( 5 x + 4 ) ^ { 1 / 3 } = 5$

Simplify. Write the answer in exponential form without negative exponents. - $14 x ^ { 2 / 7 } \cdot 2 x ^ { - 9 / 4 }$

Simplify. - $\sqrt [ 3 ] { 7 } \sqrt [ 3 ] { 147 }$

Simplify. - $\sqrt [ 3 ] { \frac { 9 x ^ { 3 } y ^ { 11 } } { 3 x ^ { 9 } y ^ { 3 } } }$

Simplify. - $\frac { \sqrt { 75 } } { \sqrt { 3 } }$

Solve the problem. -A balloon is secured to rope that is staked to the ground. A breeze blows the balloon so that the rope is taut while the balloon is directly above a flag pole that is 70 feet from where the rope is staked down. Find the Altitude of the balloon if the rope is 120 feet long.

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. - $\sqrt [ 4 ] { \frac { 1 } { 625 } }$

Simplify. Write the answer in exponential form without negative exponents. - $\left( \frac { 4 ^ { 3 } x ^ { 1 / 4 } y ^ { 5 } } { x ^ { 1 / 4 } } \right) ^ { 1 / 3 }$

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

Write as an absolute value. - $\sqrt { \left( 11 x ^ { 6 } - 7 y ^ { 4 } \right) ^ { 2 } }$

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. - $\sqrt [ 5 ] { \frac { 243 } { 32 } }$

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

Simplify. - 53253\sqrt [ 3 ] { 5 } \sqrt [ 3 ] { 25 }35​325​

Evaluate if possible. If the expression is not a real number, so state. - (27−1/3)0\left( 27 ^ { - 1 / 3 } \right) ^ { 0 }(27−1/3)0

Simplify. - 13+33\frac { 1 } { \sqrt { 3 } } + \frac { \sqrt { 3 } } { 3 }3​1​+33​​

Factor. Write the answer without negative exponents. - y1/5−y11/5y ^ { 1 / 5 } - y ^ { 11 / 5 }y1/5−y11/5

Write the expression in exponential form. Assume that all variables represent positive real numbers. - 4x12y119\sqrt [ 9 ] { 4 x ^ { 12 } y ^ { 11 } }94x12y11​

Simplify. Write the answer in exponential form without negative exponents. - x−9/2x ^ { - 9 / 2 }x−9/2

Simplify. - 14x98x\sqrt { 14 x } \sqrt { 98 x }14x​98x​