Question 1

Add or subtract.
-(4 - 9i)+ (6 + 7i)

Accepted Answer

A) 10 - 2i 
B) 10 + 2i 
C) -10 + 2i 
D) -2 + 16i 
A) 10 - 2i 
B) 10 + 2i 
C) -10 + 2i 
D) -2 + 16i

Question 2

Evaluate if possible. If the expression is not a real number, so state.
-$- 32 ^ { 1 / 5 }$

Accepted Answer

A) 32 
B) -8 
C) -2 
D) 16 
A) 32 
B) -8 
C) -2 
D) 16

Question 3

Solve. You will have to square both sides of the equation twice to eliminate all radicals.
-$\sqrt { 5 x + 4 } = \sqrt { 3 x - 3 } - 3$

Accepted Answer

A) 28 
B) - 1, 5 
C) 1, 28 
D) no real solution 
A) 28 
B) - 1, 5 
C) 1, 28 
D) no real solution

Question 4

Divide.
-$\frac { 17 - 30 i } { 5 - 2 i }$

Accepted Answer

A) -4 + 5i 
B) 5 - 4i 
C) 5 + 4i 
D) -4 - 5i 
A) -4 + 5i 
B) 5 - 4i 
C) 5 + 4i 
D) -4 - 5i

Question 5

Use absolute value to evaluate.
-$$\sqrt { ( 15.7 ) ^ { 2 } }$$

Accepted Answer

A) -15.7 
B) 15.7 
C) 246.49 
D) not a real number 
A) -15.7 
B) 15.7 
C) 246.49 
D) not a real number

Question 6

Simplify.
-75 + 9 27 - 5 147

Accepted Answer

A) 30 3 
B) 3 3 
C) -27 3 
D) -3 3 
A) 30 3 
B) 3 3 
C) -27 3 
D) -3 3

Question 7

Solve and check your solution(s). If the equation has no real solution, so state.
-$\sqrt { 12 y - 12 } = y + 2$

Accepted Answer

A) 3 
B) -4 
C) -3 
D) 4 
A) 3 
B) -4 
C) -3 
D) 4

Question 8

Find the indicated value of the function. Use your calculator to approximate irrational numbers. Round irrational
numbers to the nearest thousandth.
-$\text { Find } f ( - 3 ) \text { if } f ( x ) = \sqrt { x + 19 }$

Accepted Answer

A) 4 
B) 2 
C) -4 
D) not a real number 
A) 4 
B) 2 
C) -4 
D) not a real number

Question 9

Simplify. Assume all variables represent positive real numbers.
-$\frac { 1 } { \sqrt { 2 x } }$

Accepted Answer

A)  $\frac { \sqrt { 2 x } } { 2 x }$ 
B)  $\frac { \sqrt { 2 x } } { 4 x ^ { 2 } }$ 
C)  $\sqrt { 2 x }$ 
D) 1 
A)  $\frac { \sqrt { 2 x } } { 2 x }$ 
B)  $\frac { \sqrt { 2 x } } { 4 x ^ { 2 } }$ 
C)  $\sqrt { 2 x }$ 
D) 1

Question 10

Simplify.
-$8 \sqrt { 2 } - 5 \sqrt { 2 }$

Accepted Answer

A)  $3 \sqrt { 4 }$ 
B)  $13 \sqrt { 2 }$ 
C)  $3 \sqrt { 2 }$ 
D)  $- 40 \sqrt { 4 }$ 
A)  $3 \sqrt { 4 }$ 
B)  $13 \sqrt { 2 }$ 
C)  $3 \sqrt { 2 }$ 
D)  $- 40 \sqrt { 4 }$

Question 11

Solve the problem.
-The formula for the period of a pendulum on the moon isn is T $\mathrm { T } = \frac { \pi \sqrt { 3 } \ell } { 2 },$ , wher whee T is the period in seconds, and L is its length in feet. Find the period of a pendulum whose length is 10 feet. (Round to the nearest hundredth.)

Accepted Answer

A) 2.74 sec 
B) 8.60 sec 
C) 4.97 sec 
D) 2.72 sec 
A) 2.74 sec 
B) 8.60 sec 
C) 4.97 sec 
D) 2.72 sec

Question 12

Simplify.
-$\sqrt [ 4 ] { 162 }$

Accepted Answer

A)  $3 \sqrt [ 4 ] { 2 }$ 
B)  $3 \sqrt { 2 }$ 
C)  $2 \sqrt [ 4 ] { 3 }$ 
D)  $2 \sqrt { 3 }$ 
A)  $3 \sqrt [ 4 ] { 2 }$ 
B)  $3 \sqrt { 2 }$ 
C)  $2 \sqrt [ 4 ] { 3 }$ 
D)  $2 \sqrt { 3 }$

Question 13

Simplify.
-$x ^ { 2 } \sqrt [ 3 ] { 64 x ^ { 4 } y ^ { 2 } } - x ^ { 3 } \sqrt [ 3 ] { xy ^ { 2 } } + 9 x \sqrt [ 3 ] { x ^ { 7 } y ^ { 2 } }$

Accepted Answer

A)  $- 6 x ^ { 3 } \sqrt [ 3 ] { x y ^ { 2 } }$ 
B)  $13 x ^ { 3 } \sqrt [ 3 ] { x y ^ { 2 } }$ 
C)  $12 x ^ { 3 } \sqrt [ 3 ] { x y ^ { 2 } }$ 
D)  $12 x ^ { 3 } \sqrt [ 3 ] { y ^ { 2 } }$ 
A)  $- 6 x ^ { 3 } \sqrt [ 3 ] { x y ^ { 2 } }$ 
B)  $13 x ^ { 3 } \sqrt [ 3 ] { x y ^ { 2 } }$ 
C)  $12 x ^ { 3 } \sqrt [ 3 ] { x y ^ { 2 } }$ 
D)  $12 x ^ { 3 } \sqrt [ 3 ] { y ^ { 2 } }$

Question 14

Evaluate.
-$\text { ¡51 }$

Accepted Answer

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

Question 15

Write the expression as a complex number in the form a + bi.
-$\sqrt { - 36 } + \sqrt { - 64 }$

Accepted Answer

A) 0 - 14i 
B)  $- 14 + 0 i$ 
C) 0 + 14i 
D) 0 + 48i 
A) 0 - 14i 
B)  $- 14 + 0 i$ 
C) 0 + 14i 
D) 0 + 48i

Question 16

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)  $\sqrt { 10 }$ 
B)  $3 \sqrt { 2 }$ 
C)  $\sqrt { 66 }$ 
D)  $2 \sqrt { 17 }$ 
A)  $\sqrt { 10 }$ 
B)  $3 \sqrt { 2 }$ 
C)  $\sqrt { 66 }$ 
D)  $2 \sqrt { 17 }$

Question 17

Evaluate.
-$\mathrm { i } ^ { 38 }$

Accepted Answer

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

Question 18

Divide.
-$\frac { 7 - 10 i } { - 5 i }$

Accepted Answer

A)  $- 2 - \frac { 7 } { 5 } i$ 
B)  $2 + \frac { 7 } { 5 } i$ 
C)  $- \frac { 7 } { 5 } + 2 i$ 
D)  $\frac { 7 } { 5 } - 2 i$ 
A)  $- 2 - \frac { 7 } { 5 } i$ 
B)  $2 + \frac { 7 } { 5 } i$ 
C)  $- \frac { 7 } { 5 } + 2 i$ 
D)  $\frac { 7 } { 5 } - 2 i$

Question 19

Evaluate if possible. If the expression is not a real number, so state.
-$( 16 ) ^ { - 5 / 4 }$

Accepted Answer

A) 32 
B)  $- \frac { 1 } { 32 }$ 
C) -32 
D)  $\frac { 1 } { 32 }$ 
A) 32 
B)  $- \frac { 1 } { 32 }$ 
C) -32 
D)  $\frac { 1 } { 32 }$

Question 20

Simplify.
-$\sqrt { 65 }$

Accepted Answer

A) 13 
B)  $5 \sqrt { 13 }$ 
C)  $13 \sqrt { 5 }$ 
D)  $\sqrt { 65 }$ 
A) 13 
B)  $5 \sqrt { 13 }$ 
C)  $13 \sqrt { 5 }$ 
D)  $\sqrt { 65 }$

Add or subtract. -(4 - 9i)+ (6 + 7i)

Evaluate if possible. If the expression is not a real number, so state. - $- 32 ^ { 1 / 5 }$

Solve. You will have to square both sides of the equation twice to eliminate all radicals. - $\sqrt { 5 x + 4 } = \sqrt { 3 x - 3 } - 3$

Divide. - $\frac { 17 - 30 i } { 5 - 2 i }$

Use absolute value to evaluate. - $\sqrt { ( 15.7 ) ^ { 2 } }$

Simplify. -75 + 9 27 - 5 147

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt { 12 y - 12 } = y + 2$

Find the indicated value of the function. Use your calculator to approximate irrational numbers. Round irrational numbers to the nearest thousandth. - $\text { Find } f ( - 3 ) \text { if } f ( x ) = \sqrt { x + 19 }$

Simplify. Assume all variables represent positive real numbers. - $\frac { 1 } { \sqrt { 2 x } }$

Simplify. - $8 \sqrt { 2 } - 5 \sqrt { 2 }$

Solve the problem. -The formula for the period of a pendulum on the moon isn is T $\mathrm { T } = \frac { \pi \sqrt { 3 } \ell } { 2 },$ , wher whee T is the period in seconds, and L is its length in feet. Find the period of a pendulum whose length is 10 feet. (Round to the nearest hundredth.)

Simplify. - $\sqrt [ 4 ] { 162 }$

Simplify. - $x ^ { 2 } \sqrt [ 3 ] { 64 x ^ { 4 } y ^ { 2 } } - x ^ { 3 } \sqrt [ 3 ] { xy ^ { 2 } } + 9 x \sqrt [ 3 ] { x ^ { 7 } y ^ { 2 } }$

Evaluate. - $\text { ¡51 }$

Write the expression as a complex number in the form a + bi. - $\sqrt { - 36 } + \sqrt { - 64 }$

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.

Evaluate. - $\mathrm { i } ^ { 38 }$

Divide. - $\frac { 7 - 10 i } { - 5 i }$

Evaluate if possible. If the expression is not a real number, so state. - $( 16 ) ^ { - 5 / 4 }$

Simplify. - $\sqrt { 65 }$

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

Add or subtract. -(4 - 9i)+ (6 + 7i)

Evaluate if possible. If the expression is not a real number, so state. - −321/5- 32 ^ { 1 / 5 }−321/5

Solve. You will have to square both sides of the equation twice to eliminate all radicals. - 5x+4=3x−3−3\sqrt { 5 x + 4 } = \sqrt { 3 x - 3 } - 35x+4​=3x−3​−3

Divide. - 17−30i5−2i\frac { 17 - 30 i } { 5 - 2 i }5−2i17−30i​

Use absolute value to evaluate. - (15.7)2\sqrt { ( 15.7 ) ^ { 2 } }(15.7)2​