Question 1

Perform the indicated operations. Assume that all variables represent positive numbers.
-$( \sqrt { 3 } - 4 ) ( \sqrt { 2 } - 6 )$

Accepted Answer

A)  $\sqrt { 6 } - 10 \sqrt { 2 } + 24$ 
B)  $\sqrt { 6 } - 6 \sqrt { 3 } - 4 \sqrt { 2 } + 24$ 
C)  $\sqrt { 6 } + 24$ 
D)  $- 9 \sqrt { 6 } + 24$ 
A)  $\sqrt { 6 } - 10 \sqrt { 2 } + 24$ 
B)  $\sqrt { 6 } - 6 \sqrt { 3 } - 4 \sqrt { 2 } + 24$ 
C)  $\sqrt { 6 } + 24$ 
D)  $- 9 \sqrt { 6 } + 24$

Question 2

Rationalize the numerator and simplify. Assume all variables represent positive real numbers.
-$\frac { \sqrt { 6 } + 7 } { \sqrt { 7 } }$

Accepted Answer

A)  $\frac { - 43 } { \sqrt { 42 } + 7 \sqrt { 7 } }$ 
B)  $\frac { 13 } { \sqrt { 42 } - 7 \sqrt { 7 } }$ 
C)  $\frac { 42 } { 3 \sqrt { 42 } + 6 \sqrt { 7 } }$ 
D)  $\frac { - 43 } { \sqrt { 42 } - 7 \sqrt { 7 } }$ 
A)  $\frac { - 43 } { \sqrt { 42 } + 7 \sqrt { 7 } }$ 
B)  $\frac { 13 } { \sqrt { 42 } - 7 \sqrt { 7 } }$ 
C)  $\frac { 42 } { 3 \sqrt { 42 } + 6 \sqrt { 7 } }$ 
D)  $\frac { - 43 } { \sqrt { 42 } - 7 \sqrt { 7 } }$

Question 3

Write in terms of i.
-$\sqrt { - 324 }$

Accepted Answer

A)  $18 \mathrm { i }$ 
B)  $- \mathrm { i } \sqrt { 18 }$ 
C)  $\pm 18$ 
D)  $- 18 \mathrm { i }$ 
A)  $18 \mathrm { i }$ 
B)  $- \mathrm { i } \sqrt { 18 }$ 
C)  $\pm 18$ 
D)  $- 18 \mathrm { i }$

Question 4

Perform the indicated operation and simplify. Write the result in the form a $a + bi$
-$\sqrt { - 81 }$

Accepted Answer

A)  $0 + 9 \mathrm { i }$ 
B)  $9 + 0 \mathrm { i }$ 
C)  $0 - 9 \mathrm { i }$ 
D)  $0 - \mathrm { i } \sqrt { 9 }$ 
A)  $0 + 9 \mathrm { i }$ 
B)  $9 + 0 \mathrm { i }$ 
C)  $0 - 9 \mathrm { i }$ 
D)  $0 - \mathrm { i } \sqrt { 9 }$

Question 5

Add or subtract. Assume all variables represent positive real numbers.
-$- 2 \sqrt { 6 } - 9 \sqrt { 54 }$

Accepted Answer

A)  $- 11 \sqrt { 6 }$ 
B)  $- 29 \sqrt { 6 }$ 
C)  $- 25 \sqrt { 6 }$ 
D)  $29 \sqrt { 6 }$ 
A)  $- 11 \sqrt { 6 }$ 
B)  $- 29 \sqrt { 6 }$ 
C)  $- 25 \sqrt { 6 }$ 
D)  $29 \sqrt { 6 }$

Question 6

Use the product rule to multiply. Assume all variables represent positive real numbers.
-$\sqrt { 3 } \cdot \sqrt { 2 }$

Accepted Answer

A)  6 
B)  $\sqrt { 6 }$ 
C)  $\sqrt { 3 + 2 }$ 
D)  $\sqrt { 5 }$ 
A)  6 
B)  $\sqrt { 6 }$ 
C)  $\sqrt { 3 + 2 }$ 
D)  $\sqrt { 5 }$

Question 7

Add or subtract. Assume all variables represent positive real numbers.
-$9 \sqrt [ 3 ] { x ^ { 3 } y ^ { 10 } } + 4 x y \sqrt [ 3 ] { 27 y ^ { 7 } }$

Accepted Answer

A)  $13 x y 4 \sqrt [ 3 ] { 27 y }$ 
B)  $13 x ^ { 2 } y ^ { 4 } \sqrt [ 3 ] { y }$ 
C)  $21 x ^ { 2 } y ^ { 3 } \sqrt [ 3 ] { 3 y }$ 
D)  $21 \mathrm { xy } ^ { 3 } \sqrt [ 3 ] { \mathrm { y } }$ 
A)  $13 x y 4 \sqrt [ 3 ] { 27 y }$ 
B)  $13 x ^ { 2 } y ^ { 4 } \sqrt [ 3 ] { y }$ 
C)  $21 x ^ { 2 } y ^ { 3 } \sqrt [ 3 ] { 3 y }$ 
D)  $21 \mathrm { xy } ^ { 3 } \sqrt [ 3 ] { \mathrm { y } }$

Question 8

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\sqrt [ 3 ] { \frac { 10 } { 9 x ^ { 2 } } }$

Accepted Answer

A)  $\frac { \sqrt [ 3 ] { 810 x } } { 81 }$ 
B)  $\frac { \sqrt [ 3 ] { 30 x } } { 3 x }$ 
C)  $\frac { \sqrt [ 3 ] { 810 x ^ { 2 } } } { 9 x }$ 
D)  $\frac { \sqrt [ 3 ] { 90 x } } { 9 x }$ 
A)  $\frac { \sqrt [ 3 ] { 810 x } } { 81 }$ 
B)  $\frac { \sqrt [ 3 ] { 30 x } } { 3 x }$ 
C)  $\frac { \sqrt [ 3 ] { 810 x ^ { 2 } } } { 9 x }$ 
D)  $\frac { \sqrt [ 3 ] { 90 x } } { 9 x }$

Question 9

Use the product rule to multiply. Assume all variables represent positive real numbers.
-$\sqrt { 11 } \cdot \sqrt { 11 }$

Accepted Answer

A)  $\sqrt { 22 }$ 
B)  $\sqrt { 11 }$ 
C)  11 
D)  $\sqrt { 121 }$ 
A)  $\sqrt { 22 }$ 
B)  $\sqrt { 11 }$ 
C)  11 
D)  $\sqrt { 121 }$

Question 10

Solve.
-$9 \sqrt { \mathrm { x } ^ { 2 } - 80 \mathrm { x } } = \mathrm { x } ^ { 2 } - 80 \mathrm { x }$

Accepted Answer

A)  $0,80 , \frac { 81 } { 80 }$ 
B)  $0,80,81 , - 1$ 
C)  $\varnothing$ 
D)  $0,80 , - \frac { 81 } { 80 }$ 
A)  $0,80 , \frac { 81 } { 80 }$ 
B)  $0,80,81 , - 1$ 
C)  $\varnothing$ 
D)  $0,80 , - \frac { 81 } { 80 }$

Question 11

Write in terms of i.
-$\sqrt { - 49 }$

Accepted Answer

A)  iv $\sqrt { 7 }$ 
B)  $- 7 i$ 
C)  $7 \mathrm { i }$ 
D)  $\pm 7$ 
A)  iv $\sqrt { 7 }$ 
B)  $- 7 i$ 
C)  $7 \mathrm { i }$ 
D)  $\pm 7$

Question 12

Solve the problem.
-Find the distance between the points (2, 2) and (6, -6).

Accepted Answer

A)  12 units 
B)  48 units 
C)  $48 \sqrt { 3 }$ units 
D)  $4 \sqrt { 5 }$ units 
A)  12 units 
B)  48 units 
C)  $48 \sqrt { 3 }$ units 
D)  $4 \sqrt { 5 }$ units

Question 13

Simplify the radical expression. Assume that all variables represent positive real numbers.
-$\sqrt [ 5 ] { 1701 }$

Accepted Answer

A)  $7 \sqrt [ 5 ] { 3 }$ 
B)  $3 \sqrt [ 5 ] { 7 }$ 
C)  $3 \sqrt { 7 }$ 
D)  $7 \sqrt { 3 }$ 
A)  $7 \sqrt [ 5 ] { 3 }$ 
B)  $3 \sqrt [ 5 ] { 7 }$ 
C)  $3 \sqrt { 7 }$ 
D)  $7 \sqrt { 3 }$

Question 14

Simplify the radical expression. Assume that all variables represent positive real numbers.
-$\sqrt [ 3 ] { 54 }$

Accepted Answer

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

Question 15

Find the cube root.
-$\sqrt [ 3 ] { x ^ { 21 } }$

Accepted Answer

A)  $7 x$ 
B)  $x ^ { 14 }$ 
C)  $x ^ { 3 }$ 
D)  $x ^ { 7 }$ 
A)  $7 x$ 
B)  $x ^ { 14 }$ 
C)  $x ^ { 3 }$ 
D)  $x ^ { 7 }$

Question 16

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\frac { \sqrt { s } } { \sqrt { s } + \sqrt { w } }$

Accepted Answer

A)  $\frac { s + s \sqrt { w } } { s + w }$ 
B)  $\frac { s - s \sqrt { w } } { s - w }$ 
C)  $\frac { s + \sqrt { s w } } { s + w }$ 
D)  $\frac { s - \sqrt { s w } } { s - w }$ 
A)  $\frac { s + s \sqrt { w } } { s + w }$ 
B)  $\frac { s - s \sqrt { w } } { s - w }$ 
C)  $\frac { s + \sqrt { s w } } { s + w }$ 
D)  $\frac { s - \sqrt { s w } } { s - w }$

Question 17

Identify the domain and then graph the function.
-$f ( x ) = \sqrt [ 3 ] { x - 2 }$; use the following table.

Accepted Answer

A)  $[ 0 , \infty )$
  
B)  $( - \infty , \infty )$
  
C)  $[ - 2 , \infty )$
  
D)  $( - \infty , \infty )$
  
A)  $[ 0 , \infty )$
  
B)  $( - \infty , \infty )$
  
C)  $[ - 2 , \infty )$
  
D)  $( - \infty , \infty )$

Question 18

Multiply, and then simplify if possible. Assume all variables represent positive real numbers.
-$( \sqrt [ 3 ] { x } + 2 ) ( \sqrt [ 3 ] { x } - 3 \sqrt { x } + 3 )$

Accepted Answer

A)  $\sqrt [ 3 ] { x ^ { 2 } } + 5 \sqrt [ 3 ] { x } - 6 \sqrt { x } - 3 \sqrt [ 6 ] { x } + 6$ 
B)  $- 3 \sqrt [ 6 ] { x ^ { 5 } } + \sqrt [ 3 ] { x ^ { 2 } } + 5 \sqrt [ 3 ] { x } - 6 \sqrt { x } + 6$ 
C)  $5 \sqrt [ 3 ] { x } - 6 \sqrt { x } - 3 \sqrt [ 6 ] { x } + \sqrt [ 9 ] { x } + 6$ 
D)  $- 3 \sqrt [ 6 ] { x ^ { 5 } } + 6 \sqrt [ 3 ] { x } - 6 \sqrt { x } + 6$ 
A)  $\sqrt [ 3 ] { x ^ { 2 } } + 5 \sqrt [ 3 ] { x } - 6 \sqrt { x } - 3 \sqrt [ 6 ] { x } + 6$ 
B)  $- 3 \sqrt [ 6 ] { x ^ { 5 } } + \sqrt [ 3 ] { x ^ { 2 } } + 5 \sqrt [ 3 ] { x } - 6 \sqrt { x } + 6$ 
C)  $5 \sqrt [ 3 ] { x } - 6 \sqrt { x } - 3 \sqrt [ 6 ] { x } + \sqrt [ 9 ] { x } + 6$ 
D)  $- 3 \sqrt [ 6 ] { x ^ { 5 } } + 6 \sqrt [ 3 ] { x } - 6 \sqrt { x } + 6$

Question 19

Simplify the radical expression. Assume that all variables represent positive real numbers.
-$\frac { \sqrt { x ^ { 13 } } } { \sqrt { 25 } }$

Accepted Answer

A)  $\frac { x ^ { 6 } \sqrt { x } } { 5 }$ 
B)  $\frac { \sqrt { x ^ { 13 } } } { 5 }$ 
C)  $\frac { x \sqrt { x ^ { 11 } } } { 5 }$ 
D)  $\frac { x ^ { 6 } x } { 5 }$ 
A)  $\frac { x ^ { 6 } \sqrt { x } } { 5 }$ 
B)  $\frac { \sqrt { x ^ { 13 } } } { 5 }$ 
C)  $\frac { x \sqrt { x ^ { 11 } } } { 5 }$ 
D)  $\frac { x ^ { 6 } x } { 5 }$

Question 20

Solve.
-When an object is dropped to the ground from a height of h meters, the time it takes for the object to reach the ground is given by the equation $t = \sqrt { \frac { \mathrm { h } } { 4.9 } }$, where $t$ is measured in seconds. If an object falls $122.5$ meters before it hits the ground, find the time it took for the object to fall.

Accepted Answer

A)  $8 \mathrm { sec }$ 
B)  $6 \mathrm { sec }$ 
C)  $5 \mathrm { sec }$ 
D)  $25 \mathrm { sec }$ 
A)  $8 \mathrm { sec }$ 
B)  $6 \mathrm { sec }$ 
C)  $5 \mathrm { sec }$ 
D)  $25 \mathrm { sec }$

Perform the indicated operations. Assume that all variables represent positive numbers. - $( \sqrt { 3 } - 4 ) ( \sqrt { 2 } - 6 )$

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - $\frac { \sqrt { 6 } + 7 } { \sqrt { 7 } }$

Write in terms of i. - $\sqrt { - 324 }$

Perform the indicated operation and simplify. Write the result in the form a $a + bi$ - $\sqrt { - 81 }$

Add or subtract. Assume all variables represent positive real numbers. - $- 2 \sqrt { 6 } - 9 \sqrt { 54 }$

Use the product rule to multiply. Assume all variables represent positive real numbers. - $\sqrt { 3 } \cdot \sqrt { 2 }$

Add or subtract. Assume all variables represent positive real numbers. - $9 \sqrt [ 3 ] { x ^ { 3 } y ^ { 10 } } + 4 x y \sqrt [ 3 ] { 27 y ^ { 7 } }$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\sqrt [ 3 ] { \frac { 10 } { 9 x ^ { 2 } } }$

Use the product rule to multiply. Assume all variables represent positive real numbers. - $\sqrt { 11 } \cdot \sqrt { 11 }$

Solve. - $9 \sqrt { \mathrm { x } ^ { 2 } - 80 \mathrm { x } } = \mathrm { x } ^ { 2 } - 80 \mathrm { x }$

Write in terms of i. - $\sqrt { - 49 }$

Solve the problem. -Find the distance between the points (2, 2) and (6, -6).

Simplify the radical expression. Assume that all variables represent positive real numbers. - $\sqrt [ 5 ] { 1701 }$

Simplify the radical expression. Assume that all variables represent positive real numbers. - $\sqrt [ 3 ] { 54 }$

Find the cube root. - $\sqrt [ 3 ] { x ^ { 21 } }$

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - $\frac { \sqrt { s } } { \sqrt { s } + \sqrt { w } }$

Identify the domain and then graph the function. - $f ( x ) = \sqrt [ 3 ] { x - 2 }$ ; use the following table. $Identify the domain and then graph the function. - f ( x ) = \sqrt [ 3 ] { x - 2 } ; use the following table.$

Multiply, and then simplify if possible. Assume all variables represent positive real numbers. - $( \sqrt [ 3 ] { x } + 2 ) ( \sqrt [ 3 ] { x } - 3 \sqrt { x } + 3 )$

Simplify the radical expression. Assume that all variables represent positive real numbers. - $\frac { \sqrt { x ^ { 13 } } } { \sqrt { 25 } }$

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

Perform the indicated operations. Assume that all variables represent positive numbers. - (3−4)(2−6)( \sqrt { 3 } - 4 ) ( \sqrt { 2 } - 6 )(3​−4)(2​−6)

Rationalize the numerator and simplify. Assume all variables represent positive real numbers. - 6+77\frac { \sqrt { 6 } + 7 } { \sqrt { 7 } }7​6​+7​

Write in terms of i. - −324\sqrt { - 324 }−324​

Perform the indicated operation and simplify. Write the result in the form a a+bia + bia+bi - −81\sqrt { - 81 }−81​

Add or subtract. Assume all variables represent positive real numbers. - −26−954- 2 \sqrt { 6 } - 9 \sqrt { 54 }−26​−954​

Use the product rule to multiply. Assume all variables represent positive real numbers. - 3⋅2\sqrt { 3 } \cdot \sqrt { 2 }3​⋅2​

Add or subtract. Assume all variables represent positive real numbers. - 9x3y103+4xy27y739 \sqrt [ 3 ] { x ^ { 3 } y ^ { 10 } } + 4 x y \sqrt [ 3 ] { 27 y ^ { 7 } }93x3y10​+4xy327y7​

Rationalize the denominator and simplify. Assume that all variables represent positive real numbers. - 109x23\sqrt [ 3 ] { \frac { 10 } { 9 x ^ { 2 } } }39x210​​

Use the product rule to multiply. Assume all variables represent positive real numbers. - 11⋅11\sqrt { 11 } \cdot \sqrt { 11 }11​⋅11​

Solve. - 9x2−80x=x2−80x9 \sqrt { \mathrm { x } ^ { 2 } - 80 \mathrm { x } } = \mathrm { x } ^ { 2 } - 80 \mathrm { x }9x2−80x​=x2−80x

Write in terms of i. - −49\sqrt { - 49 }−49​