Question 1

Simplify the radical expression. Assume that all variables represent positive real numbers.
-$\sqrt { \mathrm { y } ^ { 7 } }$

Accepted Answer

A)  $y ^ { 3 } \sqrt { y }$ 
B)  $y ^ { 6 } \sqrt { y }$ 
C)  $y \sqrt { y ^ { 5 } }$ 
D)  $\sqrt { \mathrm { y } ^ { 7 } }$ 
A)  $y ^ { 3 } \sqrt { y }$ 
B)  $y ^ { 6 } \sqrt { y }$ 
C)  $y \sqrt { y ^ { 5 } }$ 
D)  $\sqrt { \mathrm { y } ^ { 7 } }$

Question 2

Use the quotient rule to divide and simplify.
-$\frac { \sqrt { 50 } } { \sqrt { 5 } }$

Accepted Answer

A)  $\frac { 1 } { \sqrt { 5 } }$ 
B)  $\sqrt { 10 }$ 
C)  $\frac { 1 } { \sqrt { 10 } }$ 
D)  $\sqrt { 5 }$ 
A)  $\frac { 1 } { \sqrt { 5 } }$ 
B)  $\sqrt { 10 }$ 
C)  $\frac { 1 } { \sqrt { 10 } }$ 
D)  $\sqrt { 5 }$

Question 3

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$\sqrt { 5 } ( \sqrt { 5 } + x \sqrt { 10 } )$

Accepted Answer

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

Question 4

Use rational exponents to write as a single radical expression.
-$\sqrt [ 7 ] { x } \cdot \sqrt { x }$

Accepted Answer

A)  $x ^ { 9 }$ 
B)  $\sqrt [ 7 ] { \mathrm { x } ^ { 2 } }$ 
C)  $\sqrt { x ^ { 9 } }$ 
D)  $\sqrt [ 14 ] { \mathrm { x } ^ { 9 } }$ 
A)  $x ^ { 9 }$ 
B)  $\sqrt [ 7 ] { \mathrm { x } ^ { 2 } }$ 
C)  $\sqrt { x ^ { 9 } }$ 
D)  $\sqrt [ 14 ] { \mathrm { x } ^ { 9 } }$

Question 5

Solve.
-$\sqrt { x ^ { 2 } - 19 } + 9 = 0$

Accepted Answer

A)  $\varnothing$ 
B)  10 
C)  $10 , - 10$ 
D)  $11 , - 11$ 
A)  $\varnothing$ 
B)  10 
C)  $10 , - 10$ 
D)  $11 , - 11$

Question 6

Use the properties of exponents to simplify the expression. Write with positive exponents.
-$z ^ { - 2 / 5 } \cdot z ^ { 3 / 5 }$

Accepted Answer

A)  $z ^ { - 1 / 5 }$ 
B)  $z ^ { 1 / 5 }$ 
C)  $z ^ { 5 / 6 }$ 
D)  $z ^ { 6 / 5 }$ 
A)  $z ^ { - 1 / 5 }$ 
B)  $z ^ { 1 / 5 }$ 
C)  $z ^ { 5 / 6 }$ 
D)  $z ^ { 6 / 5 }$

Question 7

Simplify. Assume that all variables represent any real number.
-$\sqrt { x ^ { 2 } }$

Accepted Answer

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

Question 8

Simplify the radical expression. Assume that all variables represent positive real numbers.
-$\sqrt { 12 x ^ { 2 } y }$

Accepted Answer

A)  $2 x y ^ { 2 } \sqrt { 3 }$ 
B)  $2 x ^ { 2 } \sqrt { 3 y }$ 
C)  $2 x y \sqrt { 3 }$ 
D)  $2 x \sqrt { 3 y }$ 
A)  $2 x y ^ { 2 } \sqrt { 3 }$ 
B)  $2 x ^ { 2 } \sqrt { 3 y }$ 
C)  $2 x y \sqrt { 3 }$ 
D)  $2 x \sqrt { 3 y }$

Question 9

Simplify the radical expression. Assume that all variables represent positive real numbers.
-$\frac { \sqrt [ 4 ] { 486 x ^ { 17 } } } { \sqrt [ 4 ] { 6 x } }$

Accepted Answer

A)  $3 x ^ { 4 }$ 
B)  $3 x ^ { 4 } \sqrt [ 4 ] { x }$ 
C)  $x ^ { 4 } \sqrt [ 4 ] { 3 }$ 
D)  $x ^ { 4 } \sqrt [ 4 ] { 6 }$ 
A)  $3 x ^ { 4 }$ 
B)  $3 x ^ { 4 } \sqrt [ 4 ] { x }$ 
C)  $x ^ { 4 } \sqrt [ 4 ] { 3 }$ 
D)  $x ^ { 4 } \sqrt [ 4 ] { 6 }$

Question 10

Simplify the radical expression. Assume that all variables represent positive real numbers.
-$\sqrt { 162 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } }$

Accepted Answer

A)  $9 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 2 \mathrm { k } }$ 
B)  $9 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 2 }$ 
C)  $9 q ^ { 4 } \sqrt { 2 k ^ { 7 } }$ 
D)  $9 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } \sqrt { 2 \mathrm { k } }$ 
A)  $9 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 2 \mathrm { k } }$ 
B)  $9 \mathrm { k } ^ { 3 } \mathrm { q } ^ { 4 } \sqrt { 2 }$ 
C)  $9 q ^ { 4 } \sqrt { 2 k ^ { 7 } }$ 
D)  $9 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } \sqrt { 2 \mathrm { k } }$

Question 11

Find the root. Assume that all variables represent nonnegative real numbers.
-$\sqrt [ 4 ] { 16 }$

Accepted Answer

A)  $2.497$ 
B)  not a real number 
C)  4 
D)  2 
A)  $2.497$ 
B)  not a real number 
C)  4 
D)  2

Question 12

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$\sqrt { 7 } ( \sqrt { 5 } + \sqrt { 3 } )$

Accepted Answer

A)  $8 \sqrt { 7 }$ 
B)  $\sqrt { 56 }$ 
C)  $7 \sqrt { 5 } + 7 \sqrt { 3 }$ 
D)  $\sqrt { 35 } + \sqrt { 21 }$ 
A)  $8 \sqrt { 7 }$ 
B)  $\sqrt { 56 }$ 
C)  $7 \sqrt { 5 } + 7 \sqrt { 3 }$ 
D)  $\sqrt { 35 } + \sqrt { 21 }$

Question 13

Use radical notation to write the expression. Simplify if possible.
-$6 x ^ { 1 / 4 }$

Accepted Answer

A)  $\sqrt [ 4 ] { 6 x }$ 
B)  $\frac { 3 } { 2 } x$ 
C)  $6 x$ 
D)  $6 \sqrt [ 4 ] { x }$ 
A)  $\sqrt [ 4 ] { 6 x }$ 
B)  $\frac { 3 } { 2 } x$ 
C)  $6 x$ 
D)  $6 \sqrt [ 4 ] { x }$

Question 14

Write the conjugate of the expression.
-$- 9 \sqrt { 11 } - 2 \sqrt { y }$

Accepted Answer

A)  $9 \sqrt { 11 } - 2 \sqrt { y }$ 
B)  $- 9 \sqrt { 11 } + \sqrt { y }$ 
C)  $- 9 \sqrt { 11 } + 2 \sqrt { y }$ 
D)  $9 \sqrt { 11 } + 2 \sqrt { y }$ 
A)  $9 \sqrt { 11 } - 2 \sqrt { y }$ 
B)  $- 9 \sqrt { 11 } + \sqrt { y }$ 
C)  $- 9 \sqrt { 11 } + 2 \sqrt { y }$ 
D)  $9 \sqrt { 11 } + 2 \sqrt { y }$

Question 15

Add or subtract. Assume all variables represent positive real numbers.
-$6 \sqrt [ 4 ] { 6 } + 5 \sqrt [ 3 ] { 6 }$

Accepted Answer

A)  $11 \sqrt [ 3 ] { 6 }$ 
B)  $6 \sqrt [ 4 ] { 6 } + 5 \sqrt [ 3 ] { 6 }$ 
C)  $11 \sqrt [ 4 ] { 6 }$ 
D)  $30 \sqrt [ 4 ] { 36 }$ 
A)  $11 \sqrt [ 3 ] { 6 }$ 
B)  $6 \sqrt [ 4 ] { 6 } + 5 \sqrt [ 3 ] { 6 }$ 
C)  $11 \sqrt [ 4 ] { 6 }$ 
D)  $30 \sqrt [ 4 ] { 36 }$

Question 16

Simplify. Assume that all variables represent any real number.
-$\sqrt { x ^ { 2 } - 14 x + 49 }$

Accepted Answer

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

Question 17

Rationalize the numerator and simplify. Assume all variables represent positive real numbers.
-$\frac { \sqrt { 5 } } { \sqrt { 3 x } }$

Accepted Answer

A)  $\frac { 5 } { \sqrt { 5 x } }$ 
B)  $\frac { 5 } { \sqrt { 15 x } }$ 
C)  $\frac { \sqrt { 15 x } } { 3 x }$ 
D)  $\frac { 5 } { \sqrt { 3 x } }$ 
A)  $\frac { 5 } { \sqrt { 5 x } }$ 
B)  $\frac { 5 } { \sqrt { 15 x } }$ 
C)  $\frac { \sqrt { 15 x } } { 3 x }$ 
D)  $\frac { 5 } { \sqrt { 3 x } }$

Question 18

Write with positive exponents. Simplify if possible.
-$- 32 ^ { - 4 / 5 }$

Accepted Answer

A)  not a real number 
B)  $- \frac { 1 } { 16 }$ 
C)  16 
D)  $\frac { 1 } { 16 }$ 
A)  not a real number 
B)  $- \frac { 1 } { 16 }$ 
C)  16 
D)  $\frac { 1 } { 16 }$

Question 19

Write in terms of i.
-$\sqrt { - 208 }$

Accepted Answer

A)  $- 4 \mathrm { i } \sqrt { 13 }$ 
B)  $- 4 \sqrt { 13 }$ 
C)  $4 \mathrm { i } \sqrt { 13 }$ 
D)  $4 \sqrt { 13 }$ 
A)  $- 4 \mathrm { i } \sqrt { 13 }$ 
B)  $- 4 \sqrt { 13 }$ 
C)  $4 \mathrm { i } \sqrt { 13 }$ 
D)  $4 \sqrt { 13 }$

Question 20

Solve.
-$\sqrt { x - 5 } = 7$

Accepted Answer

A)  49 
B)  54 
C)  44 
D)  144 
A)  49 
B)  54 
C)  44 
D)  144

Simplify the radical expression. Assume that all variables represent positive real numbers. - $\sqrt { \mathrm { y } ^ { 7 } }$

Use the quotient rule to divide and simplify. - $\frac { \sqrt { 50 } } { \sqrt { 5 } }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $\sqrt { 5 } ( \sqrt { 5 } + x \sqrt { 10 } )$

Use rational exponents to write as a single radical expression. - $\sqrt [ 7 ] { x } \cdot \sqrt { x }$

Solve. - $\sqrt { x ^ { 2 } - 19 } + 9 = 0$

Use the properties of exponents to simplify the expression. Write with positive exponents. - $z ^ { - 2 / 5 } \cdot z ^ { 3 / 5 }$

Simplify. Assume that all variables represent any real number. - $\sqrt { x ^ { 2 } }$

Simplify the radical expression. Assume that all variables represent positive real numbers. - $\sqrt { 12 x ^ { 2 } y }$

Simplify the radical expression. Assume that all variables represent positive real numbers. - $\frac { \sqrt [ 4 ] { 486 x ^ { 17 } } } { \sqrt [ 4 ] { 6 x } }$

Simplify the radical expression. Assume that all variables represent positive real numbers. - $\sqrt { 162 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } }$

Find the root. Assume that all variables represent nonnegative real numbers. - $\sqrt [ 4 ] { 16 }$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $\sqrt { 7 } ( \sqrt { 5 } + \sqrt { 3 } )$

Use radical notation to write the expression. Simplify if possible. - $6 x ^ { 1 / 4 }$

Write the conjugate of the expression. - $- 9 \sqrt { 11 } - 2 \sqrt { y }$

Add or subtract. Assume all variables represent positive real numbers. - $6 \sqrt [ 4 ] { 6 } + 5 \sqrt [ 3 ] { 6 }$

Simplify. Assume that all variables represent any real number. - $\sqrt { x ^ { 2 } - 14 x + 49 }$

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - $\frac { \sqrt { 5 } } { \sqrt { 3 x } }$

Write with positive exponents. Simplify if possible. - $- 32 ^ { - 4 / 5 }$

Write in terms of i. - $\sqrt { - 208 }$

Solve. - $\sqrt { x - 5 } = 7$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 10: Rational Exponents, Radicals, and Complex Numbers

Simplify the radical expression. Assume that all variables represent positive real numbers. - y7\sqrt { \mathrm { y } ^ { 7 } }y7​

Use the quotient rule to divide and simplify. - 505\frac { \sqrt { 50 } } { \sqrt { 5 } }5​50​​

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - 5(5+x10)\sqrt { 5 } ( \sqrt { 5 } + x \sqrt { 10 } )5​(5​+x10​)

Use rational exponents to write as a single radical expression. - x7⋅x\sqrt [ 7 ] { x } \cdot \sqrt { x }7x​⋅x​

Solve. - x2−19+9=0\sqrt { x ^ { 2 } - 19 } + 9 = 0x2−19​+9=0

Use the properties of exponents to simplify the expression. Write with positive exponents. - z−2/5⋅z3/5z ^ { - 2 / 5 } \cdot z ^ { 3 / 5 }z−2/5⋅z3/5

Simplify. Assume that all variables represent any real number. - x2\sqrt { x ^ { 2 } }x2​

Simplify the radical expression. Assume that all variables represent positive real numbers. - 12x2y\sqrt { 12 x ^ { 2 } y }12x2y​

Simplify the radical expression. Assume that all variables represent positive real numbers. - 486x1746x4\frac { \sqrt [ 4 ] { 486 x ^ { 17 } } } { \sqrt [ 4 ] { 6 x } }46x​4486x17​​

Simplify the radical expression. Assume that all variables represent positive real numbers. - 162k7q8\sqrt { 162 \mathrm { k } ^ { 7 } \mathrm { q } ^ { 8 } }162k7q8​

Find the root. Assume that all variables represent nonnegative real numbers. - 164\sqrt [ 4 ] { 16 }416​

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - 7(5+3)\sqrt { 7 } ( \sqrt { 5 } + \sqrt { 3 } )7​(5​+3​)

Use radical notation to write the expression. Simplify if possible. - 6x1/46 x ^ { 1 / 4 }6x1/4

Write the conjugate of the expression. - −911−2y- 9 \sqrt { 11 } - 2 \sqrt { y }−911​−2y​

Add or subtract. Assume all variables represent positive real numbers. - 664+5636 \sqrt [ 4 ] { 6 } + 5 \sqrt [ 3 ] { 6 }646​+536​

Simplify. Assume that all variables represent any real number. - x2−14x+49\sqrt { x ^ { 2 } - 14 x + 49 }x2−14x+49​

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - 53x\frac { \sqrt { 5 } } { \sqrt { 3 x } }3x​5​​

Write with positive exponents. Simplify if possible. - −32−4/5- 32 ^ { - 4 / 5 }−32−4/5

Write in terms of i. - −208\sqrt { - 208 }−208​

Solve. - x−5=7\sqrt { x - 5 } = 7x−5​=7