Question 1

Simplify by rationalizing the denominator. Write your answer in a +bi form.
-$\frac { 8 - 8 i } { 5 - 6 i }$

Accepted Answer

A)  $- 8 + \frac { 8 } { 11 } \mathrm { i }$ 
B)  $\frac { 8 } { 11 } + \frac { 8 } { 11 } \mathrm { i }$ 
C)  $\frac { 88 } { 61 } + \frac { 8 } { 61 } \mathrm { i }$ 
D)  $- \frac { 8 } { 61 } + \frac { 88 } { 61 } \mathrm { i }$ 
A)  $- 8 + \frac { 8 } { 11 } \mathrm { i }$ 
B)  $\frac { 8 } { 11 } + \frac { 8 } { 11 } \mathrm { i }$ 
C)  $\frac { 88 } { 61 } + \frac { 8 } { 61 } \mathrm { i }$ 
D)  $- \frac { 8 } { 61 } + \frac { 88 } { 61 } \mathrm { i }$

Question 2

Simplify by rationalizing the denominator. Write your answer in a +bi form.
-$\frac { 9 + 8 i } { 5 - 4 i }$

Accepted Answer

A)  $\frac { 13 } { 9 }$ 
B)  $\frac { 77 } { 41 } - \frac { 4 } { 41 } \mathrm { i }$ 
C)  $\frac { 77 } { 9 } - \frac { 76 } { 9 } \mathrm { i }$ 
D)  $\frac { 13 } { 41 } + \frac { 76 } { 41 } \mathrm { i }$ 
A)  $\frac { 13 } { 9 }$ 
B)  $\frac { 77 } { 41 } - \frac { 4 } { 41 } \mathrm { i }$ 
C)  $\frac { 77 } { 9 } - \frac { 76 } { 9 } \mathrm { i }$ 
D)  $\frac { 13 } { 41 } + \frac { 76 } { 41 } \mathrm { i }$

Question 3

Add or subtract the complex numbers
-$( 6 + 5 i ) - ( - 2 + i )$

Accepted Answer

A)  $8 - 4 \mathrm { i }$ 
B)  $- 8 - 4 i$ 
C)  $8 + 4 i$ 
D)  $4 + 6 i$ 
A)  $8 - 4 \mathrm { i }$ 
B)  $- 8 - 4 i$ 
C)  $8 + 4 i$ 
D)  $4 + 6 i$

Question 4

Provide an appropriate response.
-How many real square roots does any positive number have?

Accepted Answer

A)  None 
B)  One 
C)  Two 
D)  It depends on the number 
A)  None 
B)  One 
C)  Two 
D)  It depends on the number

Question 5

Solve. Check for extraneous solutions.
-$$3 x ^ { 1 / 2 } - 5 = 4$$

Accepted Answer

A)  $\{ 81 \}$ 
B)  $\{ \sqrt { 3 } \}$ 
C)  $\{ 9 \}$ 
D)  $\{ 3 \}$ 
A)  $\{ 81 \}$ 
B)  $\{ \sqrt { 3 } \}$ 
C)  $\{ 9 \}$ 
D)  $\{ 3 \}$

Question 6

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-Explain in your own words why possible solutions of radical equations must be checked.

Accepted Answer

The square of a number is equal to the s

Question 7

Simplify the radical expression. If appropriate, include absolute values.
-$$\sqrt { 9 x ^ { 2 } + 18 x + 9 }$$

Accepted Answer

A)  $- 3 x + 6$ 
B)  $3 x + 3 + \sqrt { 18 x }$ 
C)  $| 3 x + 3 |$ 
D)  $| 3 x - 3 |$ 
A)  $- 3 x + 6$ 
B)  $3 x + 3 + \sqrt { 18 x }$ 
C)  $| 3 x + 3 |$ 
D)  $| 3 x - 3 |$

Question 8

Write the word or phrase that best completes each statement or answers the question.
-$$5 \sqrt { 605 } - 2 \sqrt { 28 } + ( ? ) = 52 \sqrt { 5 } + 11 \sqrt { 7 }$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 9

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$\sqrt { 7 } ( \sqrt { 343 } - \sqrt { 7 } )$

Accepted Answer

A)  56 
B)  42 
C)  $49 - \sqrt { 7 }$ 
D)  $7 \sqrt { 7 } - 7$ 
A)  56 
B)  42 
C)  $49 - \sqrt { 7 }$ 
D)  $7 \sqrt { 7 } - 7$

Question 10

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers.
-$\sqrt { \frac { 49 } { 12 } }$

Accepted Answer

A)  $\frac { 7 \sqrt { 3 } } { 3 }$ 
B)  $\frac { 7 \sqrt { 3 } } { 6 }$ 
C)  12 
D)  $7 \sqrt { 3 }$ 
A)  $\frac { 7 \sqrt { 3 } } { 3 }$ 
B)  $\frac { 7 \sqrt { 3 } } { 6 }$ 
C)  12 
D)  $7 \sqrt { 3 }$

Question 11

Simplify.
-$\frac { \sqrt { 119 } } { \sqrt { 7 } }$

Accepted Answer

A)  7 
B)  17 
C)  $\sqrt { 17 }$ 
D)  $\sqrt { 7 }$ 
A)  7 
B)  17 
C)  $\sqrt { 17 }$ 
D)  $\sqrt { 7 }$

Question 12

Simplify. Assume all variables represent nonnegative values.
-$\frac { \sqrt { 9 } } { \sqrt { 49 } }$

Accepted Answer

A)  21 
B)  $ \frac{3}{7} $ 
C)  $ \frac{7}{3} $ 
D)  1 
A)  21 
B)  $ \frac{3}{7} $ 
C)  $ \frac{7}{3} $ 
D)  1

Question 13

Simplify the radical expression. Indicate if the expression is not a real number.
-$\sqrt { 25 }$

Accepted Answer

A)  Not a real number 
B)  12 
C)  5 
D)  6 
A)  Not a real number 
B)  12 
C)  5 
D)  6

Question 14

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$$- \sqrt [ 3 ] { 125 }$$

Accepted Answer

A)  25 
B)  -125 
C)  5 
D)  -5 
A)  25 
B)  -125 
C)  5 
D)  -5

Question 15

Simplify by rationalizing the denominator. Write your answer in a +bi form.
-$\frac { 6 - 3 i } { 5 + 7 i }$

Accepted Answer

A)  $- \frac { 17 } { 8 } - \frac { 19 } { 8 } \mathrm { i }$ 
B)  $\frac { 9 } { 74 } - \frac { 57 } { 74 } \mathrm { i }$ 
C)  $\frac { 51 } { 74 } - \frac { 27 } { 74 } \mathrm { i }$ 
D)  $- \frac { 3 } { 8 } - \frac { 19 } { 8 } \mathrm { i }$ 
A)  $- \frac { 17 } { 8 } - \frac { 19 } { 8 } \mathrm { i }$ 
B)  $\frac { 9 } { 74 } - \frac { 57 } { 74 } \mathrm { i }$ 
C)  $\frac { 51 } { 74 } - \frac { 27 } { 74 } \mathrm { i }$ 
D)  $- \frac { 3 } { 8 } - \frac { 19 } { 8 } \mathrm { i }$

Question 16

Solve the problem.
-For the function $f ( x ) = \sqrt { x ^ { 2 } - 9 x + 45 } - 1$, find all values $x$ for which $f ( x ) = 4$.

Accepted Answer

A)  $\{ 5,4 \}$ 
B)  $\{ 5 , - 4 \}$ 
C)  $\{ - 5 , - 4 \}$ 
D)  $\varnothing$ 
A)  $\{ 5,4 \}$ 
B)  $\{ 5 , - 4 \}$ 
C)  $\{ - 5 , - 4 \}$ 
D)  $\varnothing$

Question 17

Approximate to the nearest thousandth, using a calculator.
-$$- \sqrt { 5166 }$$

Accepted Answer

A)  -71.880 
B)  -5166.000 
C)  -71.875 
D)  -71.872 
A)  -71.880 
B)  -5166.000 
C)  -71.875 
D)  -71.872

Question 18

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers.
-$\frac { 3 \sqrt { 26 x } } { \sqrt { x ^ { 3 } } }$

Accepted Answer

A)  $\frac { 3 \sqrt { 26 x } } { x }$ 
B)  $3 \times \sqrt { 26 }$ 
C)  $\frac { 3 \sqrt { 26 } } { x }$ 
D)  $\frac { 78 } { x }$ 
A)  $\frac { 3 \sqrt { 26 x } } { x }$ 
B)  $3 \times \sqrt { 26 }$ 
C)  $\frac { 3 \sqrt { 26 } } { x }$ 
D)  $\frac { 78 } { x }$

Question 19

Multiply.
-$( \sqrt { 6 } - 5 ) ( \sqrt { 5 } + 6 )$

Accepted Answer

A)  $\sqrt { 30 } + 1 \sqrt { 5 } - 30$ 
B)  $\sqrt { 30 } + 6 \sqrt { 6 } - 5 \sqrt { 5 } - 30$ 
C)  $2 \sqrt { 30 } - 30$ 
D)  $\sqrt { 30 } - 30$ 
A)  $\sqrt { 30 } + 1 \sqrt { 5 } - 30$ 
B)  $\sqrt { 30 } + 6 \sqrt { 6 } - 5 \sqrt { 5 } - 30$ 
C)  $2 \sqrt { 30 } - 30$ 
D)  $\sqrt { 30 } - 30$

Question 20

Multiply the conjugates.
-$$( 2 + 3 i ) ( 2 - 3 i )$$

Accepted Answer

A)  13 
B)  $4 - 9 i$ 
C)  $- 5$ 
D)  $4 + 9 i$ 
A)  13 
B)  $4 - 9 i$ 
C)  $- 5$ 
D)  $4 + 9 i$

Simplify by rationalizing the denominator. Write your answer in a +bi form. - $\frac { 8 - 8 i } { 5 - 6 i }$

Simplify by rationalizing the denominator. Write your answer in a +bi form. - $\frac { 9 + 8 i } { 5 - 4 i }$

Add or subtract the complex numbers - $( 6 + 5 i ) - ( - 2 + i )$

Provide an appropriate response. -How many real square roots does any positive number have?

Solve. Check for extraneous solutions. - $3 x ^ { 1 / 2 } - 5 = 4$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain in your own words why possible solutions of radical equations must be checked.

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt { 9 x ^ { 2 } + 18 x + 9 }$

Write the word or phrase that best completes each statement or answers the question. - $5 \sqrt { 605 } - 2 \sqrt { 28 } + ( ? ) = 52 \sqrt { 5 } + 11 \sqrt { 7 }$

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $\sqrt { 7 } ( \sqrt { 343 } - \sqrt { 7 } )$

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers. - $\sqrt { \frac { 49 } { 12 } }$

Simplify. - $\frac { \sqrt { 119 } } { \sqrt { 7 } }$

Simplify. Assume all variables represent nonnegative values. - $\frac { \sqrt { 9 } } { \sqrt { 49 } }$

Simplify the radical expression. Indicate if the expression is not a real number. - $\sqrt { 25 }$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $- \sqrt [ 3 ] { 125 }$

Simplify by rationalizing the denominator. Write your answer in a +bi form. - $\frac { 6 - 3 i } { 5 + 7 i }$

Solve the problem. -For the function $f ( x ) = \sqrt { x ^ { 2 } - 9 x + 45 } - 1$ , find all values $x$ for which $f ( x ) = 4$ .

Approximate to the nearest thousandth, using a calculator. - $- \sqrt { 5166 }$

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers. - $\frac { 3 \sqrt { 26 x } } { \sqrt { x ^ { 3 } } }$

Multiply. - $( \sqrt { 6 } - 5 ) ( \sqrt { 5 } + 6 )$

Multiply the conjugates. - $( 2 + 3 i ) ( 2 - 3 i )$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 9: Radical Expressions and Equations

Simplify by rationalizing the denominator. Write your answer in a +bi form. - 8−8i5−6i\frac { 8 - 8 i } { 5 - 6 i }5−6i8−8i​

Simplify by rationalizing the denominator. Write your answer in a +bi form. - 9+8i5−4i\frac { 9 + 8 i } { 5 - 4 i }5−4i9+8i​

Add or subtract the complex numbers - (6+5i)−(−2+i)( 6 + 5 i ) - ( - 2 + i )(6+5i)−(−2+i)

Provide an appropriate response. -How many real square roots does any positive number have?

Solve. Check for extraneous solutions. - 3x1/2−5=43 x ^ { 1 / 2 } - 5 = 43x1/2−5=4