Question 1

Solve. You will have to square both sides of the equation twice to eliminate all radicals.
-

Accepted Answer

A)  0, 4 
B)  4 
C)  0, 8 
D)  no real solution

Question 2

Solve the problem.
-Find the length of the hypotenuse of a right triangle whose legs measure 3 feet and 12 feet in length.

Accepted Answer

A)   
B)   
C)   
D)  6 ft

Question 3

Multiply. Write the result in the form a + bi.
-(6 + 9i)(3 + 5i)

Accepted Answer

A)   
B)  63 - 3i 
C)  -27 + 57i 
D)  -27 - 57i

Question 4

Simplify. Assume all variables represent positive real numbers.
-

Accepted Answer

A)   
B)   
C)   
D)  31p

Question 5

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.
-

Accepted Answer

A)  4 
B)  -2 
C)  3 
D)  not a real number

Question 6

Multiply.
--

Accepted Answer

A)   
B)   
C)   
D)

Question 7

Multiply. Write the result in the form a + bi.
- i

Accepted Answer

A)   
B)   
C)   
D)

Question 8

Simplify.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 9

Simplify.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 10

Simplify. Write the answer in exponential form without negative exponents.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 11

Simplify. Write the answer in exponential form without negative exponents.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 12

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.
-

Accepted Answer

A)  5 
B)  5.39 
C)  5.4 
D)  not a real number

Question 13

Write the expression in exponential form. Assume that all variables represent positive real numbers.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 14

Simplify.
-

Accepted Answer

A)  12 
B)  21 
C)   
D)

Question 15

Simplify.
-

Accepted Answer

A)   
B)   
C)   
D)  not a real number

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.
-

Accepted Answer

A)   
B)   
C)   
D)  not a real number

Question 17

Write the expression in radical form. Assume that all variables represent positive real numbers.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 18

Evaluate if possible. If the expression is not a real number, so state.
-

Accepted Answer

A)  10 
B)  5 
C)  20 
D)  40

Question 19

Solve and check your solution(s). If the equation has no real solution, so state.
-

Accepted Answer

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

Question 20

Solve and check your solution(s). If the equation has no real solution, so state.
-

Accepted Answer

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

Exam 11: Roots, Radicals, and Complex Numbers

Solve. You will have to square both sides of the equation twice to eliminate all radicals. -

Solve the problem. -Find the length of the hypotenuse of a right triangle whose legs measure 3 feet and 12 feet in length.

Multiply. Write the result in the form a + bi. -(6 + 9i) (3 + 5i)

Simplify. Assume all variables represent positive real numbers. -

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. -

Multiply. --

Multiply. Write the result in the form a + bi. - i

Simplify. -

Simplify. -

Simplify. Write the answer in exponential form without negative exponents. -

Simplify. Write the answer in exponential form without negative exponents. -

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. -

Write the expression in exponential form. Assume that all variables represent positive real numbers. -

Simplify. -

Simplify. -

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. -

Write the expression in radical form. Assume that all variables represent positive real numbers. -

Evaluate if possible. If the expression is not a real number, so state. -

Solve and check your solution(s) . If the equation has no real solution, so state. -

Solve and check your solution(s) . If the equation has no real solution, so state. -