Question 1

Simplify the radical. $\sqrt { \frac { 77 } { 16 } }$

Accepted Answer

A)  $\frac { \sqrt { 11 } } { 4 }$ 
B)  $\frac { 11 \sqrt { 7 } } { 4 }$ 
C)  $\frac { \sqrt { 7 } } { 4 }$ 
D)  $\frac { \sqrt { 77 } } { 4 }$ 
E)  $\frac { 7 \sqrt { 11 } } { 4 }$ 
A)  $\frac { \sqrt { 11 } } { 4 }$ 
B)  $\frac { 11 \sqrt { 7 } } { 4 }$ 
C)  $\frac { \sqrt { 7 } } { 4 }$ 
D)  $\frac { \sqrt { 77 } } { 4 }$ 
E)  $\frac { 7 \sqrt { 11 } } { 4 }$ D

Question 2

Simplify the expression. $$i ^ { 43 }$$

Accepted Answer

A)  $- i$ 
B)  $- 1$ 
C) 1 
D)  $i$ 
E) 0 
A)  $- i$ 
B)  $- 1$ 
C) 1 
D)  $i$ 
E) 0 A

Question 3

Enter the number 1.6 in your calculator and repeatedly take the square root. What number does the display appear to be approaching?

Accepted Answer

A) 1 
B) 0 
C) 1.6 
D) 2.56 
E) The display is not approaching a number. 
A) 1 
B) 0 
C) 1.6 
D) 2.56 
E) The display is not approaching a number. A

Question 4

Simplify $\frac { 30 - \sqrt { 81 } } { 3 }$ .

Accepted Answer

A) -3 
B) 10 
C) 21 
D) 1 
E) 7 
A) -3 
B) 10 
C) 21 
D) 1 
E) 7

Question 5

Determine if $2 - 3 i$ is a solution to $$x ^ { 2 } - 5 x + 10 = 0$$ .

Accepted Answer

A)  $2 - 3 i$ is not a solution 
B)  $2 - 3 i$ is a solution 
A)  $2 - 3 i$ is not a solution 
B)  $2 - 3 i$ is a solution

Question 6

Use a calculator to approximate the value $\sqrt { 332 }$ , if possible. Round the answer to three decimal places.

Accepted Answer

A) 18.554 
B) 18.000 
C) 18.221 
D)  -18.221 
E) not a real number 
A) 18.554 
B) 18.000 
C) 18.221 
D)  -18.221 
E) not a real number

Question 7

Evaluate the radical expression (if possible)without using a calculator. $- \sqrt [ 4 ] { 2 ^ { 4 } }$

Accepted Answer

A)  2 
B)  -16 
C)  16 
D)  -2 
E) not possible 
A)  2 
B)  -16 
C)  16 
D)  -2 
E) not possible

Question 8

Multiply the expression by its conjugate and simplify. $8 \sqrt { 3 } + \sqrt { 4 }$

Accepted Answer

A)  48 
B)  70 
C)  188 
D)  20 
E)  572 
A)  48 
B)  70 
C)  188 
D)  20 
E)  572

Question 9

Use the Pythagorean Theorem to find the value of x. Round your answer to two decimal places.

Accepted Answer

A)  $x = 1.73$ 
B)  x=1 
C)  $x = 2.39$ 
D)  $x = 2.65$ 
E)  x=2 
A)  $x = 1.73$ 
B)  x=1 
C)  $x = 2.39$ 
D)  $x = 2.65$ 
E)  x=2

Question 10

Combine the radical expression, if possible. $3 \sqrt { 125 } + 4 \sqrt { 20 }$

Accepted Answer

A)  $13 \sqrt { 5 }$ 
B)  $19 \sqrt { 5 }$ 
C)  $23 \sqrt { 5 }$ 
D)  $11 \sqrt { 5 }$ 
E)  $17 \sqrt { 5 }$ 
A)  $13 \sqrt { 5 }$ 
B)  $19 \sqrt { 5 }$ 
C)  $23 \sqrt { 5 }$ 
D)  $11 \sqrt { 5 }$ 
E)  $17 \sqrt { 5 }$

Question 11

The formula $T = 2 \pi \sqrt { \frac { L } { 32 } }$ gives the time t (seconds)for a pendulum of length L (in feet)to go through one complete cycle, both forward and back (its period). Find the period of the pendulum clock if the length is 2.25 feet. Round your answer to two decimal places.

Accepted Answer

A) 1.67 seconds 
B) 0.83 second 
C) 0.27 second 
D) 0.44 second 
E) 0.79 second 
A) 1.67 seconds 
B) 0.83 second 
C) 0.27 second 
D) 0.44 second 
E) 0.79 second

Question 12

Simplify $7 i - ( 3 - 25 i ) + \sqrt { - 81 }$ and write in standard form.

Accepted Answer

A)  $- 3 - 9 i$ 
B)  $- 3 + 41 i$ 
C)  $29 i$ 
D)  $- 3 - 41 i$ 
E)  $3 + 41 i$ 
A)  $- 3 - 9 i$ 
B)  $- 3 + 41 i$ 
C)  $29 i$ 
D)  $- 3 - 41 i$ 
E)  $3 + 41 i$

Question 13

Multiply and simplify. $( 10 - 9 \sqrt { 9 t } ) ( 10 + 9 \sqrt { 9 t } )$

Accepted Answer

A)  $2000 - 162 t$ 
B)  $300 - 243 t$ 
C)  $1000 + 91 t$ 
D)  $200 + 81 t$ 
E)  $100 - 729 t$ 
A)  $2000 - 162 t$ 
B)  $300 - 243 t$ 
C)  $1000 + 91 t$ 
D)  $200 + 81 t$ 
E)  $100 - 729 t$

Question 14

Evaluate $64 ^ { - 4 / 3 }$ without using a calculator.

Accepted Answer

A)  $\frac { 1 } { 512 }$ 
B) 64 
C)  $\frac { 1 } { 64 }$ 
D)  $\frac { 1 } { 256 }$ 
E) 256 
A)  $\frac { 1 } { 512 }$ 
B) 64 
C)  $\frac { 1 } { 64 }$ 
D)  $\frac { 1 } { 256 }$ 
E) 256

Question 15

A volleyball court is 30 feet wide and 55 feet long. Find the length of the diagonal of the court. Round your answer to two decimal places.

Accepted Answer

A)  30.90 feet 
B)  62.65 feet 
C)  $170.00$ feet 
D)  $46.10$ feet 
E)  $40.62$ feet 
A)  30.90 feet 
B)  62.65 feet 
C)  $170.00$ feet 
D)  $46.10$ feet 
E)  $40.62$ feet

Question 16

In the study of calculus, students sometimes rewrite an expression by rationalizing the numerator. Rationalize the numerator for the expression below. ( Note: The results will not be in simplest radical form.) $\frac { \sqrt { 11 } - \sqrt { 3 } } { 6 }$

Accepted Answer

A)  $\frac { 56 } { 3 ( \sqrt { 11 } + \sqrt { 3 } ) }$ 
B)  $\frac { 19 } { 6 ( \sqrt { 11 } + \sqrt { 3 } ) }$ 
C)  $\frac { 7 } { 3 ( \sqrt { 11 } + \sqrt { 3 } ) }$ 
D)  $\frac { 5 } { 6 ( \sqrt { 11 } + \sqrt { 3 } ) }$ 
E)  $\frac { 4 } { 3 ( \sqrt { 11 } + \sqrt { 3 } ) }$ 
A)  $\frac { 56 } { 3 ( \sqrt { 11 } + \sqrt { 3 } ) }$ 
B)  $\frac { 19 } { 6 ( \sqrt { 11 } + \sqrt { 3 } ) }$ 
C)  $\frac { 7 } { 3 ( \sqrt { 11 } + \sqrt { 3 } ) }$ 
D)  $\frac { 5 } { 6 ( \sqrt { 11 } + \sqrt { 3 } ) }$ 
E)  $\frac { 4 } { 3 ( \sqrt { 11 } + \sqrt { 3 } ) }$

Question 17

Multiply and simplify the expression. $\sqrt [ 3 ] { 2 } ( \sqrt [ 3 ] { 4 } + 4 )$

Accepted Answer

A)  $- 2 + 4 \sqrt [ 3 ] { 2 }$ 
B)  $2 + \sqrt [ 3 ] { 2 }$ 
C)  $\sqrt [ 3 ] { 8 } + 4 \sqrt [ 3 ] { 2 }$ 
D)  $2 + 4 \sqrt [ 3 ] { 2 }$ 
E)  $2 \sqrt { 2 } + 4 \sqrt { 2 }$ 
A)  $- 2 + 4 \sqrt [ 3 ] { 2 }$ 
B)  $2 + \sqrt [ 3 ] { 2 }$ 
C)  $\sqrt [ 3 ] { 8 } + 4 \sqrt [ 3 ] { 2 }$ 
D)  $2 + 4 \sqrt [ 3 ] { 2 }$ 
E)  $2 \sqrt { 2 } + 4 \sqrt { 2 }$

Question 18

Simplify the radical $\sqrt [ 3 ] { 189 }$ , if possible.

Accepted Answer

A)  $3 \sqrt [ 3 ] { 7 }$ 
B)  $3 \sqrt { 21 }$ 
C) 3 
D)  $10 \sqrt { 3 }$ 
E)  $6 \sqrt [ 3 ] { 7 }$ 
A)  $3 \sqrt [ 3 ] { 7 }$ 
B)  $3 \sqrt { 21 }$ 
C) 3 
D)  $10 \sqrt { 3 }$ 
E)  $6 \sqrt [ 3 ] { 7 }$

Question 19

Simplify the radical expression. $\sqrt [ 5 ] { \frac { - 243 x ^ { 2 } } { y ^ { 10 } } }$

Accepted Answer

A)  $\frac { - 6 \sqrt [ 5 ] { x ^ { 2 } } } { y ^ { 8 } }$ 
B)  $\frac { - 6 \sqrt [ 5 ] { x ^ { 2 } } } { y ^ { 5 } }$ 
C)  $\frac { 9 \sqrt [ 5 ] { x ^ { 2 } } } { y ^ { 8 } }$ 
D)  $\frac { - 3 \sqrt [ 5 ] { x ^ { 2 } } } { y ^ { 2 } }$ 
E)  $\frac { - 3 \sqrt [ 5 ] { x ^ { 2 } } } { y ^ { 2 } }$ 
A)  $\frac { - 6 \sqrt [ 5 ] { x ^ { 2 } } } { y ^ { 8 } }$ 
B)  $\frac { - 6 \sqrt [ 5 ] { x ^ { 2 } } } { y ^ { 5 } }$ 
C)  $\frac { 9 \sqrt [ 5 ] { x ^ { 2 } } } { y ^ { 8 } }$ 
D)  $\frac { - 3 \sqrt [ 5 ] { x ^ { 2 } } } { y ^ { 2 } }$ 
E)  $\frac { - 3 \sqrt [ 5 ] { x ^ { 2 } } } { y ^ { 2 } }$

Question 20

Solve $8 \sqrt { x + 1 } = 9$ , if possible.

Accepted Answer

A)  x=7 
B)  $x = \frac { 1 } { 8 }$ 
C)  x= $\frac { 17 } { 64 }$ 
D)  $x = \frac { 9 } { 8 }$ 
E) no solution 
A)  x=7 
B)  $x = \frac { 1 } { 8 }$ 
C)  x= $\frac { 17 } { 64 }$ 
D)  $x = \frac { 9 } { 8 }$ 
E) no solution

Simplify the radical. $\sqrt { \frac { 77 } { 16 } }$

Simplify the expression. $i ^ { 43 }$

Enter the number 1.6 in your calculator and repeatedly take the square root. What number does the display appear to be approaching?

Simplify $\frac { 30 - \sqrt { 81 } } { 3 }$ .

Determine if $2 - 3 i$ is a solution to $x ^ { 2 } - 5 x + 10 = 0$ .

Use a calculator to approximate the value $\sqrt { 332 }$ , if possible. Round the answer to three decimal places.

Evaluate the radical expression (if possible)without using a calculator. $- \sqrt [ 4 ] { 2 ^ { 4 } }$

Multiply the expression by its conjugate and simplify. $8 \sqrt { 3 } + \sqrt { 4 }$

Use the Pythagorean Theorem to find the value of x. Round your answer to two decimal places.

Combine the radical expression, if possible. $3 \sqrt { 125 } + 4 \sqrt { 20 }$

The formula $T = 2 \pi \sqrt { \frac { L } { 32 } }$ gives the time t (seconds)for a pendulum of length L (in feet)to go through one complete cycle, both forward and back (its period). Find the period of the pendulum clock if the length is 2.25 feet. Round your answer to two decimal places.

Simplify $7 i - ( 3 - 25 i ) + \sqrt { - 81 }$ and write in standard form.

Multiply and simplify. $( 10 - 9 \sqrt { 9 t } ) ( 10 + 9 \sqrt { 9 t } )$

Evaluate $64 ^ { - 4 / 3 }$ without using a calculator.

A volleyball court is 30 feet wide and 55 feet long. Find the length of the diagonal of the court. Round your answer to two decimal places.

In the study of calculus, students sometimes rewrite an expression by rationalizing the numerator. Rationalize the numerator for the expression below. ( Note: The results will not be in simplest radical form.) $\frac { \sqrt { 11 } - \sqrt { 3 } } { 6 }$

Multiply and simplify the expression. $\sqrt [ 3 ] { 2 } ( \sqrt [ 3 ] { 4 } + 4 )$

Simplify the radical $\sqrt [ 3 ] { 189 }$ , if possible.

Simplify the radical expression. $\sqrt [ 5 ] { \frac { - 243 x ^ { 2 } } { y ^ { 10 } } }$

Solve $8 \sqrt { x + 1 } = 9$ , if possible.

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Exam 7: Radicals and Complex Numbers

Simplify the radical. 7716\sqrt { \frac { 77 } { 16 } }1677​​

Simplify the expression. i43i ^ { 43 }i43

Enter the number 1.6 in your calculator and repeatedly take the square root. What number does the display appear to be approaching?

Simplify 30−813\frac { 30 - \sqrt { 81 } } { 3 }330−81​​ .

Determine if 2−3i2 - 3 i2−3i is a solution to x2−5x+10=0x ^ { 2 } - 5 x + 10 = 0x2−5x+10=0 .

Use a calculator to approximate the value 332\sqrt { 332 }332​ , if possible. Round the answer to three decimal places.

Evaluate the radical expression (if possible)without using a calculator. −244- \sqrt [ 4 ] { 2 ^ { 4 } }−424​

Multiply the expression by its conjugate and simplify. 83+48 \sqrt { 3 } + \sqrt { 4 }83​+4​

Use the Pythagorean Theorem to find the value of x. Round your answer to two decimal places.

Combine the radical expression, if possible. 3125+4203 \sqrt { 125 } + 4 \sqrt { 20 }3125​+420​

Simplify 7i−(3−25i)+−817 i - ( 3 - 25 i ) + \sqrt { - 81 }7i−(3−25i)+−81​ and write in standard form.

Multiply and simplify. (10−99t)(10+99t)( 10 - 9 \sqrt { 9 t } ) ( 10 + 9 \sqrt { 9 t } )(10−99t​)(10+99t​)

Evaluate 64−4/364 ^ { - 4 / 3 }64−4/3 without using a calculator.

A volleyball court is 30 feet wide and 55 feet long. Find the length of the diagonal of the court. Round your answer to two decimal places.

In the study of calculus, students sometimes rewrite an expression by rationalizing the numerator. Rationalize the numerator for the expression below. ( Note: The results will not be in simplest radical form.) 11−36\frac { \sqrt { 11 } - \sqrt { 3 } } { 6 }611​−3​​

Multiply and simplify the expression. 23(43+4)\sqrt [ 3 ] { 2 } ( \sqrt [ 3 ] { 4 } + 4 )32​(34​+4)

Simplify the radical 1893\sqrt [ 3 ] { 189 }3189​ , if possible.

Simplify the radical expression. −243x2y105\sqrt [ 5 ] { \frac { - 243 x ^ { 2 } } { y ^ { 10 } } }5y10−243x2​​

Solve 8x+1=98 \sqrt { x + 1 } = 98x+1​=9 , if possible.

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Factoring

Rational Expressions, Equations, and Functions

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Simplify the radical. $\sqrt { \frac { 77 } { 16 } }$

Simplify the expression. $i ^ { 43 }$

Simplify $\frac { 30 - \sqrt { 81 } } { 3 }$ .

Determine if $2 - 3 i$ is a solution to $x ^ { 2 } - 5 x + 10 = 0$ .

Use a calculator to approximate the value $\sqrt { 332 }$ , if possible. Round the answer to three decimal places.

Evaluate the radical expression (if possible)without using a calculator. $- \sqrt [ 4 ] { 2 ^ { 4 } }$

Multiply the expression by its conjugate and simplify. $8 \sqrt { 3 } + \sqrt { 4 }$

Combine the radical expression, if possible. $3 \sqrt { 125 } + 4 \sqrt { 20 }$

Simplify $7 i - ( 3 - 25 i ) + \sqrt { - 81 }$ and write in standard form.

Multiply and simplify. $( 10 - 9 \sqrt { 9 t } ) ( 10 + 9 \sqrt { 9 t } )$

Evaluate $64 ^ { - 4 / 3 }$ without using a calculator.

In the study of calculus, students sometimes rewrite an expression by rationalizing the numerator. Rationalize the numerator for the expression below. ( Note: The results will not be in simplest radical form.) $\frac { \sqrt { 11 } - \sqrt { 3 } } { 6 }$

Multiply and simplify the expression. $\sqrt [ 3 ] { 2 } ( \sqrt [ 3 ] { 4 } + 4 )$

Simplify the radical $\sqrt [ 3 ] { 189 }$ , if possible.

Simplify the radical expression. $\sqrt [ 5 ] { \frac { - 243 x ^ { 2 } } { y ^ { 10 } } }$

Solve $8 \sqrt { x + 1 } = 9$ , if possible.