Question 1

Simplify.
-$\frac { \sqrt { 6 } } { 13 } + \frac { 1 } { \sqrt { 6 } }$

Accepted Answer

A)  $\frac { - 7 \sqrt { 6 } } { 6 }$ 
B)  $\frac { - 7 \sqrt { 6 } } { 13 }$ 
C)  $\frac { 19 \sqrt { 6 } } { 78 }$ 
D)  $\frac { - 7 \sqrt { 6 } } { 78 }$ 
A)  $\frac { - 7 \sqrt { 6 } } { 6 }$ 
B)  $\frac { - 7 \sqrt { 6 } } { 13 }$ 
C)  $\frac { 19 \sqrt { 6 } } { 78 }$ 
D)  $\frac { - 7 \sqrt { 6 } } { 78 }$

Question 2

Factor. Write the answer without negative exponents.
-$x ^ { 9 / 2 } + x ^ { 1 / 2 }$

Accepted Answer

A)  $x ^ { 1 / 2 } \left( x ^ { 4 } + 1 \right)$ 
B)  $x ^ { 1 / 2 } \left( x ^ { 4 } + x \right)$ 
C)  $x ^ { 1 / 2 } \left( x ^ { 9 } + 1 \right)$ 
D)  $x ^ { 1 / 2 } \left( x ^ { 9 } + x \right)$ 
A)  $x ^ { 1 / 2 } \left( x ^ { 4 } + 1 \right)$ 
B)  $x ^ { 1 / 2 } \left( x ^ { 4 } + x \right)$ 
C)  $x ^ { 1 / 2 } \left( x ^ { 9 } + 1 \right)$ 
D)  $x ^ { 1 / 2 } \left( x ^ { 9 } + x \right)$

Question 3

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.
-$$\sqrt [ 3 ] { \frac { 1 } { 27 } }$$

Accepted Answer

A) 0.19 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 5 }$ 
D) not a real number 
A) 0.19 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 5 }$ 
D) not a real number

Question 4

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

Accepted Answer

A)  $- 2 \sqrt { 5 }$ 
B) 5 
C) 1 
D) 0 
A)  $- 2 \sqrt { 5 }$ 
B) 5 
C) 1 
D) 0

Question 5

Write as an absolute value.
-$\sqrt { 49 x ^ { 2 } - 42 x y + 9 y ^ { 2 } }$

Accepted Answer

A)  $| 7 x + 3 y |$ 
B)  $7 x - 3 y$ 
C)  $| 7 x - 3 y |$ 
D)  $7 x + 3 y$ 
A)  $| 7 x + 3 y |$ 
B)  $7 x - 3 y$ 
C)  $| 7 x - 3 y |$ 
D)  $7 x + 3 y$

Question 6

Simplify. Assume all variables represent positive real numbers.
-$\sqrt { \frac { 13 p ^ { 9 } q ^ { 8 } } { 7 r } }$

Accepted Answer

A)  $\frac { p ^ { 4 } q ^ { 4 } \sqrt { 91 p r } } { 7 r }$ 
B)  $\frac { p ^ { 5 } q ^ { 4 } \sqrt { 91 r } } { 7 r }$ 
C)  $\frac { 13 p ^ { 4 } q ^ { 4 } \sqrt { 91 p r } } { 7 r }$ 
D)  $\frac { \mathrm { p } ^ { 4 } \mathrm { q } ^ { 4 } \sqrt { 91 \mathrm { pqr } } } { 7 \mathrm { r } }$ 
A)  $\frac { p ^ { 4 } q ^ { 4 } \sqrt { 91 p r } } { 7 r }$ 
B)  $\frac { p ^ { 5 } q ^ { 4 } \sqrt { 91 r } } { 7 r }$ 
C)  $\frac { 13 p ^ { 4 } q ^ { 4 } \sqrt { 91 p r } } { 7 r }$ 
D)  $\frac { \mathrm { p } ^ { 4 } \mathrm { q } ^ { 4 } \sqrt { 91 \mathrm { pqr } } } { 7 \mathrm { r } }$

Question 7

Write the word or phrase that best completes each statement or answers the question.
-$$\frac { \sqrt [ 4 ] { ( x + 7 y ) ^ { 5 } } } { \sqrt [ 5 ] { ( x + 7 y ) ^ { 4 } } }$$

Accepted Answer

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

Question 8

Evaluate if possible. If the expression is not a real number, so state.
-$125 ^ { 1 / 3 } + 25 ^ { 1 / 2 }$

Accepted Answer

A) 125 
B)  $54 \frac { 1 } { 6 }$ 
C) 10 
D) 29 
A) 125 
B)  $54 \frac { 1 } { 6 }$ 
C) 10 
D) 29

Question 9

Multiply.
-$\frac { 1 } { 2 } x ^ { - 2 } \left( 6 x ^ { 5 / 3 } - 14 x ^ { - 1 / 2 } \right)$

Accepted Answer

A)  $\frac { 3 } { x ^ { 1 / 3 } } - \frac { 7 } { x ^ { 5 / 2 } }$ 
B)  $\frac { 3 } { x ^ { 1 / 3 } } + \frac { 7 } { x ^ { 5 / 2 } }$ 
C)  $3 x ^ { 1 / 3 } + 7 x ^ { 5 / 2 }$ 
D)  $3 x ^ { 1 / 3 } - 7 x ^ { 5 / 2 }$ 
A)  $\frac { 3 } { x ^ { 1 / 3 } } - \frac { 7 } { x ^ { 5 / 2 } }$ 
B)  $\frac { 3 } { x ^ { 1 / 3 } } + \frac { 7 } { x ^ { 5 / 2 } }$ 
C)  $3 x ^ { 1 / 3 } + 7 x ^ { 5 / 2 }$ 
D)  $3 x ^ { 1 / 3 } - 7 x ^ { 5 / 2 }$

Question 10

Simplify.
-17 3 2 - 5 3 250

Accepted Answer

A) 8 3 2 
B) -8 3 2 
C) 17 3 2 - 5 3 250 
D) 12 3 2 
A) 8 3 2 
B) -8 3 2 
C) 17 3 2 - 5 3 250 
D) 12 3 2

Question 11

Simplify.
-$4 \sqrt [ 3 ] { 3 } + 2 \sqrt [ 3 ] { 3 }$

Accepted Answer

A)  $6 \sqrt [ 3 ] { 9 }$ 
B)  $6 \sqrt [ 3 ] { 3 }$ 
C)  $- 2 \sqrt [ 3 ] { 3 }$ 
D)  $6 \sqrt [ 3 ] { 6 }$ 
A)  $6 \sqrt [ 3 ] { 9 }$ 
B)  $6 \sqrt [ 3 ] { 3 }$ 
C)  $- 2 \sqrt [ 3 ] { 3 }$ 
D)  $6 \sqrt [ 3 ] { 6 }$

Question 12

Simplify.
-$\sqrt [ 4 ] { 1296 x ^ { 8 } y ^ { 16 } }$

Accepted Answer

A)  $36 x ^ { 4 } y ^ { 2 }$ 
B)  $10.645 x ^ { 2 } y ^ { 4 }$ 
C)  $6 x ^ { 2 } y ^ { 4 }$ 
D) not a real number 
A)  $36 x ^ { 4 } y ^ { 2 }$ 
B)  $10.645 x ^ { 2 } y ^ { 4 }$ 
C)  $6 x ^ { 2 } y ^ { 4 }$ 
D) not a real number

Question 13

Multiply. Write the result in the form a + bi.
-$\left( \frac { 1 } { 5 } - \frac { 1 } { 7 } \mathrm { i } \right) \left( \frac { 1 } { 2 } + \frac { 3 } { 7 } \mathrm { i } \right)$

Accepted Answer

A)  $\frac { 79 } { 490 } - \frac { 1 } { 70 } \mathrm { i }$ 
B)  $\frac { 79 } { 490 } + \frac { 11 } { 70 } \mathrm { i }$ 
C)  $\frac { 79 } { 490 } + \frac { 1 } { 70 } \mathrm { i }$ 
D)  $\frac { 79 } { 490 } - \frac { 11 } { 70 } i$ 
A)  $\frac { 79 } { 490 } - \frac { 1 } { 70 } \mathrm { i }$ 
B)  $\frac { 79 } { 490 } + \frac { 11 } { 70 } \mathrm { i }$ 
C)  $\frac { 79 } { 490 } + \frac { 1 } { 70 } \mathrm { i }$ 
D)  $\frac { 79 } { 490 } - \frac { 11 } { 70 } i$

Question 14

Find the perimeter of the figure in radical form with the radicals simplified.
-

Accepted Answer

A)  $( 70 + 7 \sqrt { 3 } ) \mathrm { m }$ 
B)  $( \sqrt { 50 } + \sqrt { 98 } + \sqrt { 147 } ) \mathrm { m }$ 
C)  $19 \sqrt { 6 } \mathrm {~m}$ 
D)  $( 12 \sqrt { 2 } + 7 \sqrt { 3 } ) \mathrm { m }$ 
A)  $( 70 + 7 \sqrt { 3 } ) \mathrm { m }$ 
B)  $( \sqrt { 50 } + \sqrt { 98 } + \sqrt { 147 } ) \mathrm { m }$ 
C)  $19 \sqrt { 6 } \mathrm {~m}$ 
D)  $( 12 \sqrt { 2 } + 7 \sqrt { 3 } ) \mathrm { m }$

Question 15

Divide.
-$\frac { 6 + 2 i } { 6 - 2 i }$

Accepted Answer

A)  $\frac { 1 } { 8 } + \frac { 3 } { 32 } \mathrm { i }$ 
B)  $\frac { 4 } { 5 } + \frac { 3 } { 5 } i$ 
C) 54 + 323 i 
D) 8 + 0i 
A)  $\frac { 1 } { 8 } + \frac { 3 } { 32 } \mathrm { i }$ 
B)  $\frac { 4 } { 5 } + \frac { 3 } { 5 } i$ 
C) 54 + 323 i 
D) 8 + 0i

Question 16

Divide.
-$\frac { 1 + 3 i } { 5 + 6 i }$

Accepted Answer

A)  $\frac { 23 } { 61 } + \frac { 9 } { 61 } \mathrm { i }$ 
B)  $- \frac { 13 } { 61 } - \frac { 21 } { 61 } \mathrm { i }$ 
C)  $- \frac { 23 } { 11 } - \frac { 9 } { 11 } \mathrm { i }$ 
D)  $\frac { 13 } { 11 } - \frac { 9 } { 11 } \mathrm { i }$ 
A)  $\frac { 23 } { 61 } + \frac { 9 } { 61 } \mathrm { i }$ 
B)  $- \frac { 13 } { 61 } - \frac { 21 } { 61 } \mathrm { i }$ 
C)  $- \frac { 23 } { 11 } - \frac { 9 } { 11 } \mathrm { i }$ 
D)  $\frac { 13 } { 11 } - \frac { 9 } { 11 } \mathrm { i }$

Question 17

Simplify.
-$( \sqrt { 12 } + 3 ) ( \sqrt { 12 } - 3 )$

Accepted Answer

A)  $12 - 2 \sqrt { 3 }$ 
B) 21 
C) 3 
D) 9 
A)  $12 - 2 \sqrt { 3 }$ 
B) 21 
C) 3 
D) 9

Question 18

Solve and check your solution(s). If the equation has no real solution, so state.
-$\sqrt { x ^ { 2 } + 44 } = 2 \sqrt { 4 x - 1 }$

Accepted Answer

A) 12, -4 
B) 6, 6 
C) 12, 4 
D) -6, 6 
A) 12, -4 
B) 6, 6 
C) 12, 4 
D) -6, 6

Question 19

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.
-$\sqrt { \frac { 1 } { 9 } }$

Accepted Answer

A)  $\frac { 1 } { 81 }$ 
B)  $\frac { 1 } { 3 }$ 
C) 3 
D) 9 
A)  $\frac { 1 } { 81 }$ 
B)  $\frac { 1 } { 3 }$ 
C) 3 
D) 9

Question 20

Find the indicated value of the function. Use your calculator to approximate irrational numbers. Round irrational
numbers to the nearest thousandth.
-$\text { Find } g ( - 3 ) \text { if } g ( x ) = \sqrt { 25 - 5 x }$

Accepted Answer

A) 6.325 
B) 5 
C) 4.472 
D) not a real number 
A) 6.325 
B) 5 
C) 4.472 
D) not a real number

Simplify. - $\frac { \sqrt { 6 } } { 13 } + \frac { 1 } { \sqrt { 6 } }$

Factor. Write the answer without negative exponents. - $x ^ { 9 / 2 } + x ^ { 1 / 2 }$

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. - $\sqrt [ 3 ] { \frac { 1 } { 27 } }$

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

Write as an absolute value. - $\sqrt { 49 x ^ { 2 } - 42 x y + 9 y ^ { 2 } }$

Simplify. Assume all variables represent positive real numbers. - $\sqrt { \frac { 13 p ^ { 9 } q ^ { 8 } } { 7 r } }$

Write the word or phrase that best completes each statement or answers the question. - $\frac { \sqrt [ 4 ] { ( x + 7 y ) ^ { 5 } } } { \sqrt [ 5 ] { ( x + 7 y ) ^ { 4 } } }$

Evaluate if possible. If the expression is not a real number, so state. - $125 ^ { 1 / 3 } + 25 ^ { 1 / 2 }$

Multiply. - $\frac { 1 } { 2 } x ^ { - 2 } \left( 6 x ^ { 5 / 3 } - 14 x ^ { - 1 / 2 } \right)$

Simplify. -17 3 2 - 5 3 250

Simplify. - $4 \sqrt [ 3 ] { 3 } + 2 \sqrt [ 3 ] { 3 }$

Simplify. - $\sqrt [ 4 ] { 1296 x ^ { 8 } y ^ { 16 } }$

Multiply. Write the result in the form a + bi. - $\left( \frac { 1 } { 5 } - \frac { 1 } { 7 } \mathrm { i } \right) \left( \frac { 1 } { 2 } + \frac { 3 } { 7 } \mathrm { i } \right)$

Find the perimeter of the figure in radical form with the radicals simplified. -

Divide. - $\frac { 6 + 2 i } { 6 - 2 i }$

Divide. - $\frac { 1 + 3 i } { 5 + 6 i }$

Simplify. - $( \sqrt { 12 } + 3 ) ( \sqrt { 12 } - 3 )$

Solve and check your solution(s). If the equation has no real solution, so state. - $\sqrt { x ^ { 2 } + 44 } = 2 \sqrt { 4 x - 1 }$

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. - $\sqrt { \frac { 1 } { 9 } }$

Find the indicated value of the function. Use your calculator to approximate irrational numbers. Round irrational numbers to the nearest thousandth. - $\text { Find } g ( - 3 ) \text { if } g ( x ) = \sqrt { 25 - 5 x }$

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

Simplify. - 613+16\frac { \sqrt { 6 } } { 13 } + \frac { 1 } { \sqrt { 6 } }136​​+6​1​

Factor. Write the answer without negative exponents. - x9/2+x1/2x ^ { 9 / 2 } + x ^ { 1 / 2 }x9/2+x1/2

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. - 1273\sqrt [ 3 ] { \frac { 1 } { 27 } }3271​​

Simplify. - 5−5\sqrt { 5 } - \sqrt { 5 }5​−5​

Write as an absolute value. - 49x2−42xy+9y2\sqrt { 49 x ^ { 2 } - 42 x y + 9 y ^ { 2 } }49x2−42xy+9y2​

Simplify. Assume all variables represent positive real numbers. - 13p9q87r\sqrt { \frac { 13 p ^ { 9 } q ^ { 8 } } { 7 r } }7r13p9q8​​

Write the word or phrase that best completes each statement or answers the question. - (x+7y)54(x+7y)45\frac { \sqrt [ 4 ] { ( x + 7 y ) ^ { 5 } } } { \sqrt [ 5 ] { ( x + 7 y ) ^ { 4 } } }5(x+7y)4​4(x+7y)5​​

Evaluate if possible. If the expression is not a real number, so state. - 1251/3+251/2125 ^ { 1 / 3 } + 25 ^ { 1 / 2 }1251/3+251/2

Multiply. - 12x−2(6x5/3−14x−1/2)\frac { 1 } { 2 } x ^ { - 2 } \left( 6 x ^ { 5 / 3 } - 14 x ^ { - 1 / 2 } \right)21​x−2(6x5/3−14x−1/2)