Question 1

Add or subtract. Assume all variables represent nonnegative real numbers.
-$8 z ^ { 2 } \sqrt [ 4 ] { 10 z ^ { 3 } } + 2 z ^ { 2 } \sqrt [ 4 ] { 10 z ^ { 3 } }$

Accepted Answer

A)  $10 z ^ { 3 } \sqrt [ 4 ] { 10 z }$ 
B)  $- 10 z ^ { 2 } \sqrt [ 4 ] { 10 z ^ { 3 } }$ 
C)  $10 z ^ { 2 } \sqrt [ 4 ] { 10 z ^ { 3 } }$ 
D)  Cannot simplify 
A)  $10 z ^ { 3 } \sqrt [ 4 ] { 10 z }$ 
B)  $- 10 z ^ { 2 } \sqrt [ 4 ] { 10 z ^ { 3 } }$ 
C)  $10 z ^ { 2 } \sqrt [ 4 ] { 10 z ^ { 3 } }$ 
D)  Cannot simplify

Question 2

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$- \sqrt [ 4 ] { 81 }$

Accepted Answer

A)  -9 
B) -2 
C)  -3 
D)  Not a real number 
A)  -9 
B) -2 
C)  -3 
D)  Not a real number

Question 3

Add or subtract. Assume all variables represent nonnegative real numbers.
-$$8 \sqrt [ 5 ] { \mathrm { m } ^ { 11 } \mathrm { p } ^ { 7 } } - 2 \mathrm {~m} ^ { 2 } \mathrm { p } \sqrt [ 5 ] { \mathrm { mp } ^ { 2 } }$$

Accepted Answer

A)  $10 m ^ { 2 } p \sqrt [ 5 ] { m p ^ { 2 } }$ 
B)  $6 m ^ { 2 } p \sqrt [ 5 ] { m p ^ { 2 } }$ 
C)  6 
D)  Cannot simplify 
A)  $10 m ^ { 2 } p \sqrt [ 5 ] { m p ^ { 2 } }$ 
B)  $6 m ^ { 2 } p \sqrt [ 5 ] { m p ^ { 2 } }$ 
C)  6 
D)  Cannot simplify

Question 4

Evaluate the radical function at the given value of the variable.
-$$f ( x ) = 5 + 2 \sqrt [ 6 ] { 3 t - 48 }$$

Accepted Answer

A)  $[ 16 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , 16 )$ 
D)  $[ - 16 , \infty )$ 
A)  $[ 16 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , 16 )$ 
D)  $[ - 16 , \infty )$

Question 5

Multiply.
-$$( 5 - 3 \sqrt { 5 } ) ^ { 2 }$$

Accepted Answer

A)  $70 + 30 \sqrt { 5 }$ 
B)  $70 - 30 \sqrt { 5 }$ 
C)  $25 + 9 \sqrt { 5 }$ 
D)  $25 - 9 \sqrt { 5 }$ 
A)  $70 + 30 \sqrt { 5 }$ 
B)  $70 - 30 \sqrt { 5 }$ 
C)  $25 + 9 \sqrt { 5 }$ 
D)  $25 - 9 \sqrt { 5 }$

Question 6

Add or subtract.
-$- 3 \sqrt { 32 } - 4 \sqrt { 8 }$

Accepted Answer

A)  $- 4 \sqrt { 2 }$ 
B)  $- 20 \sqrt { 2 }$ 
C)  $4 \sqrt { 2 }$ 
D)  $20 \sqrt { 2 }$ 
A)  $- 4 \sqrt { 2 }$ 
B)  $- 20 \sqrt { 2 }$ 
C)  $4 \sqrt { 2 }$ 
D)  $20 \sqrt { 2 }$

Question 7

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$$\sqrt [ 3 ] { x } \cdot \sqrt [ 3 ] { x ^ { 14 } }$$

Accepted Answer

A)  $x ^ { 6 }$ 
B)  $x ^ { 4 }$ 
C)  $x ^ { 5 }$ 
D)  $5 x$ 
A)  $x ^ { 6 }$ 
B)  $x ^ { 4 }$ 
C)  $x ^ { 5 }$ 
D)  $5 x$

Question 8

Multiply.
--19i ∙ 3i

Accepted Answer

A)  -57i 
B)  -57 
C)  57 
D)  57i 
A)  -57i 
B)  -57 
C)  57 
D)  57i

Question 9

Multiply the conjugates.
-$$( 9 + \sqrt { 5 } ) ( 9 - \sqrt { 5 } )$$

Accepted Answer

A)  $86 - 18 \sqrt { 5 }$ 
B)  $86 + 18 \sqrt { 5 }$ 
C)  86 
D)  76 
A)  $86 - 18 \sqrt { 5 }$ 
B)  $86 + 18 \sqrt { 5 }$ 
C)  86 
D)  76

Question 10

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-Tell whether the statement is true or false. If it is false, give the correct answer. Explain
your answer. Assume that x represents a positive real number. $\sqrt { x } \cdot \sqrt { x } = x$

Accepted Answer

The statement is true. @#LAT-DLM&. By th

Question 11

Find the missing number.
-$\sqrt { 8 } \cdot \sqrt { ? } = 4$

Accepted Answer

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

Question 12

Rationalize the denominator and simplify.
-$\frac { \sqrt { 5 } } { \sqrt { 3 } + 7 }$

Accepted Answer

A)  $\frac { \sqrt { 15 } - 7 \sqrt { 5 } } { - 46 }$ 
B)  $\frac { \sqrt { 15 } - 7 \sqrt { 5 } } { 10 }$ 
C)  $\frac { 3 \sqrt { 15 } + 3 \sqrt { 5 } } { 21 }$ 
D)  $\frac { \sqrt { 15 } + 7 \sqrt { 5 } } { - 46 }$ 
A)  $\frac { \sqrt { 15 } - 7 \sqrt { 5 } } { - 46 }$ 
B)  $\frac { \sqrt { 15 } - 7 \sqrt { 5 } } { 10 }$ 
C)  $\frac { 3 \sqrt { 15 } + 3 \sqrt { 5 } } { 21 }$ 
D)  $\frac { \sqrt { 15 } + 7 \sqrt { 5 } } { - 46 }$

Question 13

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$\sqrt { 14 m ^ { 5 } } \sqrt { 7 m ^ { 15 } }$

Accepted Answer

A)  $7 \mathrm {~m} ^ { 9 } \sqrt { 2 }$ 
B)  $14 m ^ { 7 } \sqrt { 7 }$ 
C)  $7 \mathrm {~m} ^{11}$ 
D)  $7 \mathrm {~m} ^{10} \sqrt { 2 }$ 
A)  $7 \mathrm {~m} ^ { 9 } \sqrt { 2 }$ 
B)  $14 m ^ { 7 } \sqrt { 7 }$ 
C)  $7 \mathrm {~m} ^{11}$ 
D)  $7 \mathrm {~m} ^{10} \sqrt { 2 }$

Question 14

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-$\sqrt { - 108 }$

Accepted Answer

A)  $- 6 \sqrt { - 3 }$ 
B)  $- 6 \sqrt { 3 }$ 
C)  $6 \sqrt { 3 }$ 
D)  Not a real number 
A)  $- 6 \sqrt { - 3 }$ 
B)  $- 6 \sqrt { 3 }$ 
C)  $6 \sqrt { 3 }$ 
D)  Not a real number

Question 15

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. The easiest way to simplify the expression $\sqrt [ 3 ] { \frac { 9 } { 4 } }$ is to multiply both the numerator and denominator of $\frac { \sqrt [ 3 ] { 9 } } { \sqrt [ 3 ] { 4 } }$ by $\sqrt [ 3 ] { 4 }$

Accepted Answer

The statement is false. The easiest way

Question 16

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-What is the smallest power to which you can raise both sides of the radical equation $\sqrt [ n ] { 7 x - 5 } = \sqrt [ m ] { - 1 - 6 x }$ so that the radicals are eliminated. Assume that $m$ and $n$ are relatively prime.
A) $\mathrm { mn }$
B) $\frac { 1 } { m } + \frac { 1 } { n }$
C) $\frac { \mathrm { m } + \mathrm { n } } { \mathrm { mn } }$
D) $m + n$

Accepted Answer

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

Question 17

Choose the one alternative that best completes the statement or answers the question.
Multiply. Assume all variables represent nonnegative real numbers.
-$\sqrt { 3 } ( \sqrt { 5 } - 3 \sqrt { 6 } )$

Accepted Answer

A)  $\sqrt { 15 } - 3 \sqrt { 18 }$ 
B)  $\sqrt { 15 } + 9 \sqrt { 2 }$ 
C)  $\sqrt { 15 } + 3 \sqrt { 18 }$ 
D)  $\sqrt { 15 } - 9 \sqrt { 2 }$ 
A)  $\sqrt { 15 } - 3 \sqrt { 18 }$ 
B)  $\sqrt { 15 } + 9 \sqrt { 2 }$ 
C)  $\sqrt { 15 } + 3 \sqrt { 18 }$ 
D)  $\sqrt { 15 } - 9 \sqrt { 2 }$

Question 18

Simplify. Assume all variables represent nonnegative values.
-$\frac { \sqrt { 26 } } { \sqrt { 2 } }$

Accepted Answer

A)  $\sqrt { 2 }$ 
B)  13 
C)  $\sqrt { 13 }$ 
D)  2 
A)  $\sqrt { 2 }$ 
B)  13 
C)  $\sqrt { 13 }$ 
D)  2

Question 19

Add or subtract. Assume all variables represent nonnegative real numbers.
-$\sqrt { 6 a } - 7 \sqrt { 150 a } - 5 \sqrt { 216 a }$

Accepted Answer

A)  $- 64 \sqrt { 372 a }$ 
B)  $- 12 \sqrt { 372 a }$ 
C)  $- 64 \sqrt { 6 a }$ 
D)  $- 12 \sqrt { 6 a }$ 
A)  $- 64 \sqrt { 372 a }$ 
B)  $- 12 \sqrt { 372 a }$ 
C)  $- 64 \sqrt { 6 a }$ 
D)  $- 12 \sqrt { 6 a }$

Question 20

Provide an appropriate response.
-$\frac { \sqrt [ 7 ] { z ^ { 4 } } } { \sqrt [ 9 ] { z ^ { 4 } } }$

Accepted Answer

A)  $\frac { \sqrt [ 7 ] { z ^ { 4 } } } { \sqrt [ 9 ] { z ^ { 4 } } }$ 
B)  $\sqrt [ 63 ] { z ^ { 8 } }$ 
C)  $\sqrt [ 16 ] { \mathrm { z } ^ { 4 } }$ 
D)  $\sqrt [ 2 ] { \mathrm { z } ^ { 4 } }$ 
A)  $\frac { \sqrt [ 7 ] { z ^ { 4 } } } { \sqrt [ 9 ] { z ^ { 4 } } }$ 
B)  $\sqrt [ 63 ] { z ^ { 8 } }$ 
C)  $\sqrt [ 16 ] { \mathrm { z } ^ { 4 } }$ 
D)  $\sqrt [ 2 ] { \mathrm { z } ^ { 4 } }$

Add or subtract. Assume all variables represent nonnegative real numbers. - $8 z ^ { 2 } \sqrt [ 4 ] { 10 z ^ { 3 } } + 2 z ^ { 2 } \sqrt [ 4 ] { 10 z ^ { 3 } }$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $- \sqrt [ 4 ] { 81 }$

Add or subtract. Assume all variables represent nonnegative real numbers. - $8 \sqrt [ 5 ] { \mathrm { m } ^ { 11 } \mathrm { p } ^ { 7 } } - 2 \mathrm {~m} ^ { 2 } \mathrm { p } \sqrt [ 5 ] { \mathrm { mp } ^ { 2 } }$

Evaluate the radical function at the given value of the variable. - $f ( x ) = 5 + 2 \sqrt [ 6 ] { 3 t - 48 }$

Multiply. - $( 5 - 3 \sqrt { 5 } ) ^ { 2 }$

Add or subtract. - $- 3 \sqrt { 32 } - 4 \sqrt { 8 }$

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $\sqrt [ 3 ] { x } \cdot \sqrt [ 3 ] { x ^ { 14 } }$

Multiply. --19i ∙ 3i

Multiply the conjugates. - $( 9 + \sqrt { 5 } ) ( 9 - \sqrt { 5 } )$

Find the missing number. - $\sqrt { 8 } \cdot \sqrt { ? } = 4$

Rationalize the denominator and simplify. - $\frac { \sqrt { 5 } } { \sqrt { 3 } + 7 }$

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $\sqrt { 14 m ^ { 5 } } \sqrt { 7 m ^ { 15 } }$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. - $\sqrt { - 108 }$

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - $\sqrt { 3 } ( \sqrt { 5 } - 3 \sqrt { 6 } )$

Simplify. Assume all variables represent nonnegative values. - $\frac { \sqrt { 26 } } { \sqrt { 2 } }$

Add or subtract. Assume all variables represent nonnegative real numbers. - $\sqrt { 6 a } - 7 \sqrt { 150 a } - 5 \sqrt { 216 a }$

Provide an appropriate response. - $\frac { \sqrt [ 7 ] { z ^ { 4 } } } { \sqrt [ 9 ] { z ^ { 4 } } }$

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

Add or subtract. Assume all variables represent nonnegative real numbers. - 8z210z34+2z210z348 z ^ { 2 } \sqrt [ 4 ] { 10 z ^ { 3 } } + 2 z ^ { 2 } \sqrt [ 4 ] { 10 z ^ { 3 } }8z2410z3​+2z2410z3​

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - −814- \sqrt [ 4 ] { 81 }−481​

Add or subtract. Assume all variables represent nonnegative real numbers. - 8m11p75−2 m2pmp258 \sqrt [ 5 ] { \mathrm { m } ^ { 11 } \mathrm { p } ^ { 7 } } - 2 \mathrm {~m} ^ { 2 } \mathrm { p } \sqrt [ 5 ] { \mathrm { mp } ^ { 2 } }85m11p7​−2 m2p5mp2​

Evaluate the radical function at the given value of the variable. - f(x)=5+23t−486f ( x ) = 5 + 2 \sqrt [ 6 ] { 3 t - 48 }f(x)=5+263t−48​

Multiply. - (5−35)2( 5 - 3 \sqrt { 5 } ) ^ { 2 }(5−35​)2

Add or subtract. - −332−48- 3 \sqrt { 32 } - 4 \sqrt { 8 }−332​−48​

Choose the one alternative that best completes the statement or answers the question. Multiply. Assume all variables represent nonnegative real numbers. - x3⋅x143\sqrt [ 3 ] { x } \cdot \sqrt [ 3 ] { x ^ { 14 } }3x​⋅3x14​