Question 1

Evaluate.
-$\mathrm { i } ^ { 12 }$

Accepted Answer

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

Question 2

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

Accepted Answer

A) 2 
B) -2 
C) 3, 8 
D) 2, 38 
A) 2 
B) -2 
C) 3, 8 
D) 2, 38

Question 3

Evaluate if possible. If the expression is not a real number, so state.
-$16 ^ { 1 / 2 }$

Accepted Answer

A) 16 
B) 4 
C) 8 
D) 2 
A) 16 
B) 4 
C) 8 
D) 2

Question 4

Simplify.
-$3 \sqrt { \frac { x ^ { 18 } } { y ^ { 7 } } } + \frac { 7 x ^ { 9 } } { y ^ { 3 } } \sqrt { \frac { 1 } { y } }$

Accepted Answer

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

Question 5

Solve the problem.
-For the functionstions $f ( x ) = \sqrt { x ^ { 2 } - 5 x + 6 } \text { and } g ( x ) = \sqrt { x - 2 },$ , fin fid all real values of x where f(x)= g(x).

Accepted Answer

A) -4, -2 
B) 2, 4 
C) -2, 4 
D) no real solution 
A) -4, -2 
B) 2, 4 
C) -2, 4 
D) no real solution

Question 6

Simplify.
-$\sqrt [ 5 ] { 32 x ^ { 3 } y ^ { 17 } }$

Accepted Answer

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

Question 7

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

Accepted Answer

A)  $11 \sqrt { 10 }$ 
B)  $11 \sqrt { 2 }$ 
C)  $44 \sqrt { 10 }$ 
D)  $22 \sqrt { 10 }$ 
A)  $11 \sqrt { 10 }$ 
B)  $11 \sqrt { 2 }$ 
C)  $44 \sqrt { 10 }$ 
D)  $22 \sqrt { 10 }$

Question 8

Solve and check your solution(s). If the equation has no real solution, so state.
-$\sqrt { 5 x - 4 } - 4 = 0$

Accepted Answer

A) 16 
B)  $\frac { 12 } { 5 }$ 
C)  $\frac { 16 } { 5 }$ 
D) 4 
A) 16 
B)  $\frac { 12 } { 5 }$ 
C)  $\frac { 16 } { 5 }$ 
D) 4

Question 9

Solve the problem.
-Find the length of the hypotenuse of a right triangle whose legs measure 12 feet and 12 feet in length.

Accepted Answer

A)  $2 \sqrt { 6 } \mathrm { ft }$ 
B)  $12 \sqrt { 2 } \mathrm { ft }$ 
C) 12 ft 
D)  $24 \sqrt { 2 } \mathrm { ft }$ 
A)  $2 \sqrt { 6 } \mathrm { ft }$ 
B)  $12 \sqrt { 2 } \mathrm { ft }$ 
C) 12 ft 
D)  $24 \sqrt { 2 } \mathrm { ft }$

Question 10

Solve. You will have to square both sides of the equation twice to eliminate all radicals.
-$\sqrt { 6 x + 3 } = \sqrt { 4 x + 3 } - 1$

Accepted Answer

A)  $- \frac { 11 } { 2 } , 3$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $- \frac { 1 } { 2 } , \frac { 11 } { 2 }$ 
D) no real solution 
A)  $- \frac { 11 } { 2 } , 3$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $- \frac { 1 } { 2 } , \frac { 11 } { 2 }$ 
D) no real solution

Question 11

Simplify.
-$\frac { \sqrt [ 3 ] { 192 } } { \sqrt [ 3 ] { 3 } }$

Accepted Answer

A)  $4 \sqrt [ 3 ] { 3 }$ 
B) 4 
C)  $\sqrt [ 3 ] { 64 }$ 
D)  $\sqrt [ 3 ] { \frac { 192 } { 3 } }$ 
A)  $4 \sqrt [ 3 ] { 3 }$ 
B) 4 
C)  $\sqrt [ 3 ] { 64 }$ 
D)  $\sqrt [ 3 ] { \frac { 192 } { 3 } }$

Question 12

Divide.
-$\frac { 8 - 4 i } { 5 + 9 i }$

Accepted Answer

A)  $- \frac { 1 } { 28 } + \frac { 23 } { 28 } i$ 
B)  $\frac { 76 } { 53 } - \frac { 52 } { 53 } i$ 
C)  $- \frac { 19 } { 14 } + \frac { 23 } { 28 } i$ 
D)  $\frac { 2 } { 53 } - \frac { 46 } { 53 } \mathrm { i }$ 
A)  $- \frac { 1 } { 28 } + \frac { 23 } { 28 } i$ 
B)  $\frac { 76 } { 53 } - \frac { 52 } { 53 } i$ 
C)  $- \frac { 19 } { 14 } + \frac { 23 } { 28 } i$ 
D)  $\frac { 2 } { 53 } - \frac { 46 } { 53 } \mathrm { i }$

Question 13

Simplify. Assume all variables represent positive real numbers.
-$\frac { 4 } { \sqrt { 5 } }$

Accepted Answer

A) 29 
B)  $4 \sqrt { 5 }$ 
C)  $\frac { 4 \sqrt { 5 } } { 5 }$ 
D)  $\frac { 16 \sqrt { 5 } } { 5 }$ 
A) 29 
B)  $4 \sqrt { 5 }$ 
C)  $\frac { 4 \sqrt { 5 } } { 5 }$ 
D)  $\frac { 16 \sqrt { 5 } } { 5 }$

Question 14

Add or subtract.
-(5 - 4i)+ (-5 + 4i)

Accepted Answer

A) -10 - 8i 
B)  $10 - 8 \mathrm { i }$ 
C) 0 
D) -10 + 8i 
A) -10 - 8i 
B)  $10 - 8 \mathrm { i }$ 
C) 0 
D) -10 + 8i

Question 15

Solve the problem.
-Use the Pythagorean Theorem to find the length of the unknown side of the triangle. Write the answer as a radical in simplified form.

Accepted Answer

A)  $3 \sqrt { 5 }$ 
B) 18 
C) 3 
D)  $3 \sqrt { 2 }$ 
A)  $3 \sqrt { 5 }$ 
B) 18 
C) 3 
D)  $3 \sqrt { 2 }$

Question 16

Find the indicated value of the function. Use your calculator to approximate irrational numbers. Round irrational
numbers to the nearest thousandth.
-$\text { Find } r ( 18 ) \text { if } r ( x ) = \frac { x } { 3 } + \sqrt { 2 x } - 2$

Accepted Answer

A) 14 
B) -2 
C) 10 
D) 2 
A) 14 
B) -2 
C) 10 
D) 2

Question 17

Simplify.
-$\sqrt { 5 } ( \sqrt { 35 } + \sqrt { 5 } )$

Accepted Answer

A)  $25 \sqrt { 7 } + 5$ 
B)  $5 \sqrt { 7 } + 25$ 
C)  $5 \sqrt { 7 } + 5$ 
D) 35 + 25 
A)  $25 \sqrt { 7 } + 5$ 
B)  $5 \sqrt { 7 } + 25$ 
C)  $5 \sqrt { 7 } + 5$ 
D) 35 + 25

Question 18

Simplify. Assume all variables represent positive real numbers.
-$\frac { 1 } { \sqrt { 23 } }$

Accepted Answer

A)  $\frac { 1 + \sqrt { 23 } } { 23 }$ 
B)  $1 + \sqrt { 23 }$ 
C)  $\frac { \sqrt { 23 } } { 23 }$ 
D)  $\sqrt { 23 }$ 
A)  $\frac { 1 + \sqrt { 23 } } { 23 }$ 
B)  $1 + \sqrt { 23 }$ 
C)  $\frac { \sqrt { 23 } } { 23 }$ 
D)  $\sqrt { 23 }$

Question 19

Solve and check your solution(s). If the equation has no real solution, so state.
-$\sqrt [ 4 ] { s + 1 } + 8 = 0$

Accepted Answer

A) 8 
B) - 4096 
C) 4096 
D) no real solution 
A) 8 
B) - 4096 
C) 4096 
D) no real solution

Question 20

Simplify. Assume all variables represent positive real numbers.
-$\frac { \sqrt { 13 } } { \sqrt { 11 } }$

Accepted Answer

A)  $\frac { \sqrt { 143 } } { 11 }$ 
B)  $\sqrt { 13 }$ 
C)  $\frac { \sqrt { 143 } } { 121 }$ 
D)  $\sqrt { 143 }$ 
A)  $\frac { \sqrt { 143 } } { 11 }$ 
B)  $\sqrt { 13 }$ 
C)  $\frac { \sqrt { 143 } } { 121 }$ 
D)  $\sqrt { 143 }$

Evaluate. - $\mathrm { i } ^ { 12 }$

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

Evaluate if possible. If the expression is not a real number, so state. - $16 ^ { 1 / 2 }$

Simplify. - $3 \sqrt { \frac { x ^ { 18 } } { y ^ { 7 } } } + \frac { 7 x ^ { 9 } } { y ^ { 3 } } \sqrt { \frac { 1 } { y } }$

Solve the problem. -For the functionstions $f ( x ) = \sqrt { x ^ { 2 } - 5 x + 6 } \text { and } g ( x ) = \sqrt { x - 2 },$ , fin fid all real values of x where f(x)= g(x).

Simplify. - $\sqrt [ 5 ] { 32 x ^ { 3 } y ^ { 17 } }$

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

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt { 5 x - 4 } - 4 = 0$

Solve the problem. -Find the length of the hypotenuse of a right triangle whose legs measure 12 feet and 12 feet in length.

Solve. You will have to square both sides of the equation twice to eliminate all radicals. - $\sqrt { 6 x + 3 } = \sqrt { 4 x + 3 } - 1$

Simplify. - $\frac { \sqrt [ 3 ] { 192 } } { \sqrt [ 3 ] { 3 } }$

Divide. - $\frac { 8 - 4 i } { 5 + 9 i }$

Simplify. Assume all variables represent positive real numbers. - $\frac { 4 } { \sqrt { 5 } }$

Add or subtract. -(5 - 4i)+ (-5 + 4i)

Solve the problem. -Use the Pythagorean Theorem to find the length of the unknown side of the triangle. Write the answer as a radical in simplified form.

Find the indicated value of the function. Use your calculator to approximate irrational numbers. Round irrational numbers to the nearest thousandth. - $\text { Find } r ( 18 ) \text { if } r ( x ) = \frac { x } { 3 } + \sqrt { 2 x } - 2$

Simplify. - $\sqrt { 5 } ( \sqrt { 35 } + \sqrt { 5 } )$

Simplify. Assume all variables represent positive real numbers. - $\frac { 1 } { \sqrt { 23 } }$

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt [ 4 ] { s + 1 } + 8 = 0$

Simplify. Assume all variables represent positive real numbers. - $\frac { \sqrt { 13 } } { \sqrt { 11 } }$

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

Evaluate. - i12\mathrm { i } ^ { 12 }i12

Solve. You will have to square both sides of the equation twice to eliminate all radicals. - 2x+5−x−2=3\sqrt { 2 x + 5 } - \sqrt { x - 2 } = 32x+5​−x−2​=3

Evaluate if possible. If the expression is not a real number, so state. - 161/216 ^ { 1 / 2 }161/2

Simplify. - 3x18y7+7x9y31y3 \sqrt { \frac { x ^ { 18 } } { y ^ { 7 } } } + \frac { 7 x ^ { 9 } } { y ^ { 3 } } \sqrt { \frac { 1 } { y } }3y7x18​​+y37x9​y1​​

Solve the problem. -For the functionstions f(x)=x2−5x+6 and g(x)=x−2,f ( x ) = \sqrt { x ^ { 2 } - 5 x + 6 } \text { and } g ( x ) = \sqrt { x - 2 },f(x)=x2−5x+6​ and g(x)=x−2​, , fin fid all real values of x where f(x)= g(x).

Simplify. - 32x3y175\sqrt [ 5 ] { 32 x ^ { 3 } y ^ { 17 } }532x3y17​