Question 1

Provide an appropriate response.(True or false)
-i3 = -i

Accepted Answer

A) True 
 B)False

Question 2

Solve the problem.
-For the function $f ( x ) = 5 \sqrt { x - 3 } - 5 \sqrt { 2 x - 4 }$, find all values $x$ for which $f ( x ) = 5$.

Accepted Answer

A)  5 
B)  4 
C)  $- 5$ 
D)  $\varnothing$ 
A)  5 
B)  4 
C)  $- 5$ 
D)  $\varnothing$

Question 3

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-A student tries to solve $\sqrt { x + 8 } = \sqrt { x } + 5$ by squaring both sides and gets $x + 8 = x + 25$. Why is this not correct?

Accepted Answer

Squaring t

Question 4

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers.
-$\frac { 2 } { \sqrt { 2 } }$

Accepted Answer

A)  1 
B)  $\sqrt { 2 }$ 
C)  $2 \sqrt { 2 }$ 
D)  2 
A)  1 
B)  $\sqrt { 2 }$ 
C)  $2 \sqrt { 2 }$ 
D)  2

Question 5

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$\sqrt { \mathrm { m } ^ { 21 } \mathrm { n }^{ 12} }$

Accepted Answer

A)  $\mathrm { m } ^ { 10 } \mathrm { n } ^ { 6 }$ 
B)  $m ^{10}n^ 6 \sqrt { m }$ 
C)  $\mathrm { m }^{ 10} \mathrm { n } ^{12} \sqrt { \mathrm { m } }$ 
D)  $\mathrm { m } ^ { 11 } \mathrm { n } ^7$ 
A)  $\mathrm { m } ^ { 10 } \mathrm { n } ^ { 6 }$ 
B)  $m ^{10}n^ 6 \sqrt { m }$ 
C)  $\mathrm { m }^{ 10} \mathrm { n } ^{12} \sqrt { \mathrm { m } }$ 
D)  $\mathrm { m } ^ { 11 } \mathrm { n } ^7$

Question 6

Simplify the radical expression. Indicate if the expression is not a real number.
-$- \sqrt { \frac { 576 } { 25 } }$

Accepted Answer

A)  $\frac { 24 } { 5 }$ 
B)  Not a real number 
C)  $- \frac { 24 } { 5 }$ 
D)  $- \frac { 288 } { 12 }$ 
A)  $\frac { 24 } { 5 }$ 
B)  Not a real number 
C)  $- \frac { 24 } { 5 }$ 
D)  $- \frac { 288 } { 12 }$

Question 7

Find the missing complex number.
-$$( 4 - 6 i ) ( ? ) = 8 + 3 i$$

Accepted Answer

A)  $- \frac { 7 } { 20 } + \frac { 3 } { 2 } \mathrm { i }$ 
B)  $- \frac { 5 } { 2 } + \frac { 3 } { 2 } i$ 
C)  $\frac { 25 } { 13 } + \frac { 18 } { 13 } \mathrm { i }$ 
D)  $\frac { 7 } { 26 } + \frac { 15 } { 13 }$ i 
A)  $- \frac { 7 } { 20 } + \frac { 3 } { 2 } \mathrm { i }$ 
B)  $- \frac { 5 } { 2 } + \frac { 3 } { 2 } i$ 
C)  $\frac { 25 } { 13 } + \frac { 18 } { 13 } \mathrm { i }$ 
D)  $\frac { 7 } { 26 } + \frac { 15 } { 13 }$ i

Question 8

Evaluate the radical function at the given value of the variable.
-$f ( x ) = \sqrt { x + 7 } + \sqrt { x } ;$ find $f ( 9 )$

Accepted Answer

A)  7 
B)  2 
C)  5 
D)  4 
A)  7 
B)  2 
C)  5 
D)  4

Question 9

Find the missing complex number.
-$$\frac { ? } { 6 + 6 i } = 7 - 9 i$$

Accepted Answer

A)  $- 12 + 96 i$ 
B)  $96 + 12 \mathrm { i }$ 
C)  $96 - 12 \mathrm { i }$ 
D)  $- 54 \mathrm { i } ^ { 2 } - 12 \mathrm { i } + 42$ 
A)  $- 12 + 96 i$ 
B)  $96 + 12 \mathrm { i }$ 
C)  $96 - 12 \mathrm { i }$ 
D)  $- 54 \mathrm { i } ^ { 2 } - 12 \mathrm { i } + 42$

Question 10

Simplify the radical expression. If appropriate, include absolute values.
-$$\sqrt { 4 x ^ { 2 } + 20 x + 25 }$$

Accepted Answer

A)  $| 2 x | + 5$ 
B)  $| 2 x + 5 |$ 
C)  $2 x + 5$ 
D)  $2 x + \sqrt { 10 x }$ 
A)  $| 2 x | + 5$ 
B)  $| 2 x + 5 |$ 
C)  $2 x + 5$ 
D)  $2 x + \sqrt { 10 x }$

Question 11

Multiply.
-$\sqrt { - 13 } \cdot \sqrt { - 7 }$

Accepted Answer

A)  $- \sqrt { 91 } \mathrm { i }$ 
B)  $\sqrt { 91 } \mathrm { i }$ 
C)  $- \sqrt { 91 }$ 
D)  $\sqrt { 91 }$ 
A)  $- \sqrt { 91 } \mathrm { i }$ 
B)  $\sqrt { 91 } \mathrm { i }$ 
C)  $- \sqrt { 91 }$ 
D)  $\sqrt { 91 }$

Question 12

Simplify the radical expression. If appropriate, include absolute values.
-$\sqrt { 49 x ^ { 2 } }$

Accepted Answer

A)  $- 7 | x |$ 
B)  $7 | x |$ 
C)  $7 x$ 
D)  $49 x$ 
A)  $- 7 | x |$ 
B)  $7 | x |$ 
C)  $7 x$ 
D)  $49 x$

Question 13

Find the missing number.
-$$\sqrt { ? } = 14$$

Accepted Answer

A)  392 
B)  28 
C)  16 
D)  196 
A)  392 
B)  28 
C)  16 
D)  196

Question 14

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$\sqrt { 6 } \cdot \sqrt { 25 x ^ { 3 } }$

Accepted Answer

A)  $\sqrt { 150 x ^ { 3 } }$ 
B)  $5 \sqrt { 6 x ^ { 3 } }$ 
C)  $x \sqrt { 150 x }$ 
D)  $5 x \sqrt { 6 x }$ 
A)  $\sqrt { 150 x ^ { 3 } }$ 
B)  $5 \sqrt { 6 x ^ { 3 } }$ 
C)  $x \sqrt { 150 x }$ 
D)  $5 x \sqrt { 6 x }$

Question 15

Divide.
-$( 6 + 5 i ) \div ( 9 - 6 i )$

Accepted Answer

A)  $\frac { 8 } { 45 } - \frac { 3 } { 5 } \mathrm { i }$ 
B)  $\frac { 28 } { 15 } - \frac { 3 } { 5 } \mathrm { i }$ 
C)  $\frac { 28 } { 13 } + \frac { 3 } { 13 } \mathrm { i }$ 
D)  $\frac { 8 } { 39 } + \frac { 9 } { 13 } \mathrm { i }$ 
A)  $\frac { 8 } { 45 } - \frac { 3 } { 5 } \mathrm { i }$ 
B)  $\frac { 28 } { 15 } - \frac { 3 } { 5 } \mathrm { i }$ 
C)  $\frac { 28 } { 13 } + \frac { 3 } { 13 } \mathrm { i }$ 
D)  $\frac { 8 } { 39 } + \frac { 9 } { 13 } \mathrm { i }$

Question 16

Simplify. Assume all variables represent nonnegative values.
-$\frac { \sqrt { 24 a } } { \sqrt { 4 a } }$

Accepted Answer

A)  $\sqrt { 6 }$ 
B)  $6 \sqrt { a }$ 
C)  6 
D)  $\sqrt { 6 a }$ 
A)  $\sqrt { 6 }$ 
B)  $6 \sqrt { a }$ 
C)  6 
D)  $\sqrt { 6 a }$

Question 17

Write the word or phrase that best completes each statement or answers the question.
-Find the missing radical expression. $$( 4 \sqrt [ 3 ] { 7 } - 8 \sqrt { 2 } ) + ( ? ) = 6 \sqrt [ 3 ] { 7 } - 3 \sqrt { 2 }$$

Accepted Answer

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

Question 18

Divide.
-$9 \div ( 4 \mathrm { i } )$

Accepted Answer

A)  $- \frac { 4 } { 9 } \mathrm { i }$ 
B)  $\frac { 9 } { 4 } \mathrm { i }$ 
C)  $- \frac { 9 } { 4 } \mathrm { i }$ 
D)  $\frac { 4 } { 9 } i$ 
A)  $- \frac { 4 } { 9 } \mathrm { i }$ 
B)  $\frac { 9 } { 4 } \mathrm { i }$ 
C)  $- \frac { 9 } { 4 } \mathrm { i }$ 
D)  $\frac { 4 } { 9 } i$

Question 19

Provide an appropriate response.
-If $\mathrm { n }$ is even, under what condition is $\sqrt [ n ] { \mathrm { a } }$ negative?

Accepted Answer

A)  When a is positive 
B)  Never 
C)  When a is negative 
D)  When a is zero 
A)  When a is positive 
B)  Never 
C)  When a is negative 
D)  When a is zero

Question 20

Multiply the conjugates.
-$( 6 \sqrt { 5 } - 3 \sqrt { 11 } ) ( 6 \sqrt { 5 } + 3 \sqrt { 11 } )$

Accepted Answer

A)  81 
B)  $- 3$ 
C)  279 
D)  $279 + 36 \sqrt { 55 }$ 
A)  81 
B)  $- 3$ 
C)  279 
D)  $279 + 36 \sqrt { 55 }$

Provide an appropriate response.(True or false) -i3 = -i

Solve the problem. -For the function $f ( x ) = 5 \sqrt { x - 3 } - 5 \sqrt { 2 x - 4 }$ , find all values $x$ for which $f ( x ) = 5$ .

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -A student tries to solve $\sqrt { x + 8 } = \sqrt { x } + 5$ by squaring both sides and gets $x + 8 = x + 25$ . Why is this not correct?

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers. - $\frac { 2 } { \sqrt { 2 } }$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt { \mathrm { m } ^ { 21 } \mathrm { n }^{ 12} }$

Simplify the radical expression. Indicate if the expression is not a real number. - $- \sqrt { \frac { 576 } { 25 } }$

Find the missing complex number. - $( 4 - 6 i ) ( ? ) = 8 + 3 i$

Evaluate the radical function at the given value of the variable. - $f ( x ) = \sqrt { x + 7 } + \sqrt { x } ;$ find $f ( 9 )$

Find the missing complex number. - $\frac { ? } { 6 + 6 i } = 7 - 9 i$

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt { 4 x ^ { 2 } + 20 x + 25 }$

Multiply. - $\sqrt { - 13 } \cdot \sqrt { - 7 }$

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt { 49 x ^ { 2 } }$

Find the missing number. - $\sqrt { ? } = 14$

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $\sqrt { 6 } \cdot \sqrt { 25 x ^ { 3 } }$

Divide. - $( 6 + 5 i ) \div ( 9 - 6 i )$

Simplify. Assume all variables represent nonnegative values. - $\frac { \sqrt { 24 a } } { \sqrt { 4 a } }$

Write the word or phrase that best completes each statement or answers the question. -Find the missing radical expression. $( 4 \sqrt [ 3 ] { 7 } - 8 \sqrt { 2 } ) + ( ? ) = 6 \sqrt [ 3 ] { 7 } - 3 \sqrt { 2 }$

Divide. - $9 \div ( 4 \mathrm { i } )$

Provide an appropriate response. -If $\mathrm { n }$ is even, under what condition is $\sqrt [ n ] { \mathrm { a } }$ negative?

Multiply the conjugates. - $( 6 \sqrt { 5 } - 3 \sqrt { 11 } ) ( 6 \sqrt { 5 } + 3 \sqrt { 11 } )$

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

Provide an appropriate response.(True or false) -i3 = -i

Solve the problem. -For the function f(x)=5x−3−52x−4f ( x ) = 5 \sqrt { x - 3 } - 5 \sqrt { 2 x - 4 }f(x)=5x−3​−52x−4​ , find all values xxx for which f(x)=5f ( x ) = 5f(x)=5 .

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -A student tries to solve x+8=x+5\sqrt { x + 8 } = \sqrt { x } + 5x+8​=x​+5 by squaring both sides and gets x+8=x+25x + 8 = x + 25x+8=x+25 . Why is this not correct?

Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers. - 22\frac { 2 } { \sqrt { 2 } }2​2​

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - m21n12\sqrt { \mathrm { m } ^ { 21 } \mathrm { n }^{ 12} }m21n12​

Simplify the radical expression. Indicate if the expression is not a real number. - −57625- \sqrt { \frac { 576 } { 25 } }−25576​​

Find the missing complex number. - (4−6i)(?)=8+3i( 4 - 6 i ) ( ? ) = 8 + 3 i(4−6i)(?)=8+3i

Evaluate the radical function at the given value of the variable. - f(x)=x+7+x;f ( x ) = \sqrt { x + 7 } + \sqrt { x } ;f(x)=x+7​+x​; find f(9)f ( 9 )f(9)

Find the missing complex number. - ?6+6i=7−9i\frac { ? } { 6 + 6 i } = 7 - 9 i6+6i?​=7−9i

Simplify the radical expression. If appropriate, include absolute values. - 4x2+20x+25\sqrt { 4 x ^ { 2 } + 20 x + 25 }4x2+20x+25​

Multiply. - −13⋅−7\sqrt { - 13 } \cdot \sqrt { - 7 }−13​⋅−7​

Simplify the radical expression. If appropriate, include absolute values. - 49x2\sqrt { 49 x ^ { 2 } }49x2​

Find the missing number. - ?=14\sqrt { ? } = 14?​=14

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - 6⋅25x3\sqrt { 6 } \cdot \sqrt { 25 x ^ { 3 } }6​⋅25x3​

Divide. - (6+5i)÷(9−6i)( 6 + 5 i ) \div ( 9 - 6 i )(6+5i)÷(9−6i)

Simplify. Assume all variables represent nonnegative values. - 24a4a\frac { \sqrt { 24 a } } { \sqrt { 4 a } }4a​24a​​

Write the word or phrase that best completes each statement or answers the question. -Find the missing radical expression. (473−82)+(?)=673−32( 4 \sqrt [ 3 ] { 7 } - 8 \sqrt { 2 } ) + ( ? ) = 6 \sqrt [ 3 ] { 7 } - 3 \sqrt { 2 }(437​−82​)+(?)=637​−32​

Divide. - 9÷(4i)9 \div ( 4 \mathrm { i } )9÷(4i)

Provide an appropriate response. -If n\mathrm { n }n is even, under what condition is an\sqrt [ n ] { \mathrm { a } }na​ negative?

Multiply the conjugates. - (65−311)(65+311)( 6 \sqrt { 5 } - 3 \sqrt { 11 } ) ( 6 \sqrt { 5 } + 3 \sqrt { 11 } )(65​−311​)(65​+311​)