Question 1

Multiply and simplify. $( \sqrt [ 3 ] { t } + 1 ) \left( \sqrt [ 3 ] { t ^ { 2 } } + 8 \sqrt [ 3 ] { t } - 7 \right)$

Accepted Answer

A)  $t + 9 \sqrt [ 3 ] { t ^ { 2 } } + \sqrt [ 3 ] { t } - 7$ 
B)  $t + 10 \sqrt [ 3 ] { t ^ { 2 } } + 2 \sqrt [ 3 ] { t } - b$ 
C)  $t + \sqrt [ 3 ] { t ^ { 2 } } + 7 \sqrt [ 3 ] { t } - 7$ 
D)  $+ 7 \sqrt [ 3 ] { t ^ { 2 } } - 7$ 
E)  $t + 8 \sqrt [ 3 ] { t ^ { 2 } } - 7 \sqrt [ 3 ] { t } - 7$ 
A)  $t + 9 \sqrt [ 3 ] { t ^ { 2 } } + \sqrt [ 3 ] { t } - 7$ 
B)  $t + 10 \sqrt [ 3 ] { t ^ { 2 } } + 2 \sqrt [ 3 ] { t } - b$ 
C)  $t + \sqrt [ 3 ] { t ^ { 2 } } + 7 \sqrt [ 3 ] { t } - 7$ 
D)  $+ 7 \sqrt [ 3 ] { t ^ { 2 } } - 7$ 
E)  $t + 8 \sqrt [ 3 ] { t ^ { 2 } } - 7 \sqrt [ 3 ] { t } - 7$

Question 2

The time t , in seconds, for a free falling object to fall d feet is given by $t = \sqrt { \frac { d } { 16 } }$ . If a construction worker drops a nail from a building and observes it strike a water puddle after 5 seconds, what is the height from which the nail was dropped?

Accepted Answer

A)  80 feet 
B)  25 feet 
C)  $100$ feet 
D)  $400$ feet 
E)  5 feet 
A)  80 feet 
B)  25 feet 
C)  $100$ feet 
D)  $400$ feet 
E)  5 feet

Question 3

Solve $\sqrt { x } = 3$ .

Accepted Answer

A)  x=9 
B)  x=-9 
C)  $x = - 3$ 
D)  $x = 3$ 
E)  $x = 1$ 
A)  x=9 
B)  x=-9 
C)  $x = - 3$ 
D)  $x = 3$ 
E)  $x = 1$

Question 4

A square television screen measures 39 inches across the diagonal. Find the dimensions of the screen. Round your answer to two decimal places.

Accepted Answer

A)  $19.5 \text { inches } \times 19.5 \text { inches }$ 
B)  $30.88 \text { inches } \times 30.88 \text { inches }$ 
C)  $27.58 \text { inches } \times 27.58 \text { inches }$ 
D)  $8.83 \text { inches } \times 8.83 \text { inches }$ 
E)  $29.68 \text { inches } \times 29.68 \text { inches }$ 
A)  $19.5 \text { inches } \times 19.5 \text { inches }$ 
B)  $30.88 \text { inches } \times 30.88 \text { inches }$ 
C)  $27.58 \text { inches } \times 27.58 \text { inches }$ 
D)  $8.83 \text { inches } \times 8.83 \text { inches }$ 
E)  $29.68 \text { inches } \times 29.68 \text { inches }$

Question 5

Solve $x = \sqrt { 56 - x }$ , if possible.

Accepted Answer

A)  x=8 
B)  x=56 
C)  x=7 
D)  x=-7 
E) no solution 
A)  x=8 
B)  x=56 
C)  x=7 
D)  x=-7 
E) no solution

Question 6

The demand equation for a video game is $p = 40 - \sqrt { x - 1 }$ where x is the number of units demanded per day and p is the price per game. Find the demand when the price is set at $34.4 . Round your answer to the nearest integer.

Accepted Answer

A)  31 units per day 
B)  1408 units per day 
C)  32 units per day 
D)  5536 units per day 
E)  $30$ units per day 
A)  31 units per day 
B)  1408 units per day 
C)  32 units per day 
D)  5536 units per day 
E)  $30$ units per day

Question 7

Simplify the expression $\frac { 5 ^ { 1 / 13 } } { 5 ^ { 14 / 13 } }$ .

Accepted Answer

A)  $ \frac{1}{5} $ 
B)  $\frac { 1 } { 26 }$ 
C)  5 
D)  10 
E)  26 
A)  $ \frac{1}{5} $ 
B)  $\frac { 1 } { 26 }$ 
C)  5 
D)  10 
E)  26

Question 8

Find the additive inverse of the complex number $5 - 6 i$ .

Accepted Answer

A)  $\frac { 5 } { 61 } + \frac { 5 } { 61 } i$ 
B)  $5 + 6 i$ 
C)  $- 5 - 6 i$ 
D)  $5 - 6 i$ 
E)  $- 5 + 6 i$ 
A)  $\frac { 5 } { 61 } + \frac { 5 } { 61 } i$ 
B)  $5 + 6 i$ 
C)  $- 5 - 6 i$ 
D)  $5 - 6 i$ 
E)  $- 5 + 6 i$

Question 9

State whether the number 25 is a perfect square, a perfect cube, or neither.

Accepted Answer

A) perfect square 
B) neither 
C) perfect cube 
A) perfect square 
B) neither 
C) perfect cube

Question 10

Classify the number $\sqrt { 23 }$ as rational or irrational.

Accepted Answer

A) rational 
B) irrational 
A) rational 
B) irrational

Question 11

Rationalize the denominator and simplify further, if possible. $\sqrt { \frac { 64 } { x ^ { 3 } } }$

Accepted Answer

A)  $\frac { 8 \sqrt { x } } { x ^ { 2 } }$ 
B)  $\frac { 64 } { x ^ { 2 } }$ 
C)  $\frac { 8 } { x ^ { 3 } }$ 
D)  $\frac { 8 } { x ^ { 2 } }$ 
E)  $\frac { 64 \sqrt { x } } { x }$ 
A)  $\frac { 8 \sqrt { x } } { x ^ { 2 } }$ 
B)  $\frac { 64 } { x ^ { 2 } }$ 
C)  $\frac { 8 } { x ^ { 3 } }$ 
D)  $\frac { 8 } { x ^ { 2 } }$ 
E)  $\frac { 64 \sqrt { x } } { x }$

Question 12

Rationalize the denominator of $\frac { \sqrt { y } } { 7 - \sqrt { y } }$ and simplify.

Accepted Answer

A)  $\sqrt { y }$ 
B)  $\frac { 7 + y } { 49 - y }$ 
C)  $\frac { 7 \sqrt { y } - y } { 49 - y }$ 
D)  $\frac { 7 \sqrt { y } + y } { 49 + y }$ 
E)  $\frac { 7 \sqrt { y } + y } { 49 - y }$ 
A)  $\sqrt { y }$ 
B)  $\frac { 7 + y } { 49 - y }$ 
C)  $\frac { 7 \sqrt { y } - y } { 49 - y }$ 
D)  $\frac { 7 \sqrt { y } + y } { 49 + y }$ 
E)  $\frac { 7 \sqrt { y } + y } { 49 - y }$

Question 13

Multiply and simplify. $( \sqrt [ 3 ] { 3 y } + 7 ) \left( \sqrt [ 3 ] { 9 y ^ { 2 } } - 7 \right)$

Accepted Answer

A)  $27 y ^ { 3 } + 3 \sqrt { 49 y ^ { 2 } } - 49$ 
B)  $3 y - 49$ 
C)  $3 y - 7 \sqrt [ 3 ] { 3 y } + 7 \sqrt [ 3 ] { 9 y ^ { 2 } } - 49$ 
D)  $27 y ^ { 3 } - 343$ 
E)  $3 y - 7 \sqrt [ 3 ] { 9 y } - 343$ 
A)  $27 y ^ { 3 } + 3 \sqrt { 49 y ^ { 2 } } - 49$ 
B)  $3 y - 49$ 
C)  $3 y - 7 \sqrt [ 3 ] { 3 y } + 7 \sqrt [ 3 ] { 9 y ^ { 2 } } - 49$ 
D)  $27 y ^ { 3 } - 343$ 
E)  $3 y - 7 \sqrt [ 3 ] { 9 y } - 343$

Question 14

Perform the operation(s) $( \sqrt { - 8 } ) ^ { 2 }$ and write the result in standard form.

Accepted Answer

A)  $64$ 
B)  $8 i$ 
C) 8 
D)  $- 8$ 
E)  $- 64$ 
A)  $64$ 
B)  $8 i$ 
C) 8 
D)  $- 8$ 
E)  $- 64$

Question 15

Evaluate the radical expression $- ( \sqrt { 40 } ) ^ { 2 }$ without using a calculator. If not possible, state the reason.

Accepted Answer

A)  -40 
B)  1600 
C)  -1600 
D)  40 
E) not a real number 
A)  -40 
B)  1600 
C)  -1600 
D)  40 
E) not a real number

Question 16

Find the product of $( \sqrt { t } - 6 )$ and its conjugate.

Accepted Answer

A)  $\sqrt { t } - 6$ 
B)  $t- 12$ 
C)  $\sqrt { t } - 36$ 
D)  $t - 36$ 
E)  $t + 12 \sqrt { t } - 36$ 
A)  $\sqrt { t } - 6$ 
B)  $t- 12$ 
C)  $\sqrt { t } - 36$ 
D)  $t - 36$ 
E)  $t + 12 \sqrt { t } - 36$

Question 17

Subtract $\sqrt { - 81 } - \sqrt { - 4 }$ and write in standard form.

Accepted Answer

A)  $22 i$ 
B)  $11 i$ 
C)  $\sqrt { - 7 } i$ 
D)  $7 i$ 
E)  $- 7 i$ 
A)  $22 i$ 
B)  $11 i$ 
C)  $\sqrt { - 7 } i$ 
D)  $7 i$ 
E)  $- 7 i$

Question 18

Classify the number $\sqrt { \frac { 1 } { 9 } }$ as rational or irrational.

Accepted Answer

A) rational 
B) irrational 
A) rational 
B) irrational

Question 19

Simplify the expression $\sqrt { x } - \sqrt { 16 x }$ .

Accepted Answer

A)  $- 3 \sqrt { x }$ 
B)  $\sqrt { x }$ 
C)  $- 3 x$ 
D)  $17 \sqrt { x }$ 
E)  $5 \sqrt { x }$ 
A)  $- 3 \sqrt { x }$ 
B)  $\sqrt { x }$ 
C)  $- 3 x$ 
D)  $17 \sqrt { x }$ 
E)  $5 \sqrt { x }$

Question 20

Given $f ( x )$ below, evaluate $f ( 4 - \sqrt { 2 } )$ . $f ( x ) = x ^ { 2 } - 9 x + 5$

Accepted Answer

A)  $- 13 + \sqrt { 2 }$ 
B)  $- 31 + 10 \sqrt { 2 }$ 
C)  $- 24 + 5 \sqrt { 2 }$ 
D)  $- 17 + 17 \sqrt { 2 }$ 
E)  $- 29 + 7 \sqrt { 2 }$ 
A)  $- 13 + \sqrt { 2 }$ 
B)  $- 31 + 10 \sqrt { 2 }$ 
C)  $- 24 + 5 \sqrt { 2 }$ 
D)  $- 17 + 17 \sqrt { 2 }$ 
E)  $- 29 + 7 \sqrt { 2 }$

Multiply and simplify. $( \sqrt [ 3 ] { t } + 1 ) \left( \sqrt [ 3 ] { t ^ { 2 } } + 8 \sqrt [ 3 ] { t } - 7 \right)$

The time t , in seconds, for a free falling object to fall d feet is given by $t = \sqrt { \frac { d } { 16 } }$ . If a construction worker drops a nail from a building and observes it strike a water puddle after 5 seconds, what is the height from which the nail was dropped?

Solve $\sqrt { x } = 3$ .

A square television screen measures 39 inches across the diagonal. Find the dimensions of the screen. Round your answer to two decimal places.

Solve $x = \sqrt { 56 - x }$ , if possible.

The demand equation for a video game is $p = 40 - \sqrt { x - 1 }$ where x is the number of units demanded per day and p is the price per game. Find the demand when the price is set at $34.4 . Round your answer to the nearest integer.

Simplify the expression $\frac { 5 ^ { 1 / 13 } } { 5 ^ { 14 / 13 } }$ .

Find the additive inverse of the complex number $5 - 6 i$ .

State whether the number 25 is a perfect square, a perfect cube, or neither.

Classify the number $\sqrt { 23 }$ as rational or irrational.

Rationalize the denominator and simplify further, if possible. $\sqrt { \frac { 64 } { x ^ { 3 } } }$

Rationalize the denominator of $\frac { \sqrt { y } } { 7 - \sqrt { y } }$ and simplify.

Multiply and simplify. $( \sqrt [ 3 ] { 3 y } + 7 ) \left( \sqrt [ 3 ] { 9 y ^ { 2 } } - 7 \right)$

Perform the operation(s) $( \sqrt { - 8 } ) ^ { 2 }$ and write the result in standard form.

Evaluate the radical expression $- ( \sqrt { 40 } ) ^ { 2 }$ without using a calculator. If not possible, state the reason.

Find the product of $( \sqrt { t } - 6 )$ and its conjugate.

Subtract $\sqrt { - 81 } - \sqrt { - 4 }$ and write in standard form.

Classify the number $\sqrt { \frac { 1 } { 9 } }$ as rational or irrational.

Simplify the expression $\sqrt { x } - \sqrt { 16 x }$ .

Given $f ( x )$ below, evaluate $f ( 4 - \sqrt { 2 } )$ . $f ( x ) = x ^ { 2 } - 9 x + 5$

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

Multiply and simplify. (t3+1)(t23+8t3−7)( \sqrt [ 3 ] { t } + 1 ) \left( \sqrt [ 3 ] { t ^ { 2 } } + 8 \sqrt [ 3 ] { t } - 7 \right)(3t​+1)(3t2​+83t​−7)

The time t , in seconds, for a free falling object to fall d feet is given by t=d16t = \sqrt { \frac { d } { 16 } }t=16d​​ . If a construction worker drops a nail from a building and observes it strike a water puddle after 5 seconds, what is the height from which the nail was dropped?

Solve x=3\sqrt { x } = 3x​=3 .

A square television screen measures 39 inches across the diagonal. Find the dimensions of the screen. Round your answer to two decimal places.

Solve x=56−xx = \sqrt { 56 - x }x=56−x​ , if possible.

The demand equation for a video game is p=40−x−1p = 40 - \sqrt { x - 1 }p=40−x−1​ where x is the number of units demanded per day and p is the price per game. Find the demand when the price is set at $34.4 . Round your answer to the nearest integer.

Simplify the expression 51/13514/13\frac { 5 ^ { 1 / 13 } } { 5 ^ { 14 / 13 } }514/1351/13​ .

Find the additive inverse of the complex number 5−6i5 - 6 i5−6i .

State whether the number 25 is a perfect square, a perfect cube, or neither.

Classify the number 23\sqrt { 23 }23​ as rational or irrational.

Rationalize the denominator and simplify further, if possible. 64x3\sqrt { \frac { 64 } { x ^ { 3 } } }x364​​

Rationalize the denominator of y7−y\frac { \sqrt { y } } { 7 - \sqrt { y } }7−y​y​​ and simplify.

Multiply and simplify. (3y3+7)(9y23−7)( \sqrt [ 3 ] { 3 y } + 7 ) \left( \sqrt [ 3 ] { 9 y ^ { 2 } } - 7 \right)(33y​+7)(39y2​−7)

Perform the operation(s) (−8)2( \sqrt { - 8 } ) ^ { 2 }(−8​)2 and write the result in standard form.

Evaluate the radical expression −(40)2- ( \sqrt { 40 } ) ^ { 2 }−(40​)2 without using a calculator. If not possible, state the reason.

Find the product of (t−6)( \sqrt { t } - 6 )(t​−6) and its conjugate.

Subtract −81−−4\sqrt { - 81 } - \sqrt { - 4 }−81​−−4​ and write in standard form.

Classify the number 19\sqrt { \frac { 1 } { 9 } }91​​ as rational or irrational.

Simplify the expression x−16x\sqrt { x } - \sqrt { 16 x }x​−16x​ .

Given f(x)f ( x )f(x) below, evaluate f(4−2)f ( 4 - \sqrt { 2 } )f(4−2​) . f(x)=x2−9x+5f ( x ) = x ^ { 2 } - 9 x + 5f(x)=x2−9x+5

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

Multiply and simplify. $( \sqrt [ 3 ] { t } + 1 ) \left( \sqrt [ 3 ] { t ^ { 2 } } + 8 \sqrt [ 3 ] { t } - 7 \right)$

The time t , in seconds, for a free falling object to fall d feet is given by $t = \sqrt { \frac { d } { 16 } }$ . If a construction worker drops a nail from a building and observes it strike a water puddle after 5 seconds, what is the height from which the nail was dropped?

Solve $\sqrt { x } = 3$ .

Solve $x = \sqrt { 56 - x }$ , if possible.

The demand equation for a video game is $p = 40 - \sqrt { x - 1 }$ where x is the number of units demanded per day and p is the price per game. Find the demand when the price is set at $34.4 . Round your answer to the nearest integer.

Simplify the expression $\frac { 5 ^ { 1 / 13 } } { 5 ^ { 14 / 13 } }$ .

Find the additive inverse of the complex number $5 - 6 i$ .

Classify the number $\sqrt { 23 }$ as rational or irrational.

Rationalize the denominator and simplify further, if possible. $\sqrt { \frac { 64 } { x ^ { 3 } } }$

Rationalize the denominator of $\frac { \sqrt { y } } { 7 - \sqrt { y } }$ and simplify.

Multiply and simplify. $( \sqrt [ 3 ] { 3 y } + 7 ) \left( \sqrt [ 3 ] { 9 y ^ { 2 } } - 7 \right)$

Perform the operation(s) $( \sqrt { - 8 } ) ^ { 2 }$ and write the result in standard form.

Evaluate the radical expression $- ( \sqrt { 40 } ) ^ { 2 }$ without using a calculator. If not possible, state the reason.

Find the product of $( \sqrt { t } - 6 )$ and its conjugate.

Subtract $\sqrt { - 81 } - \sqrt { - 4 }$ and write in standard form.

Classify the number $\sqrt { \frac { 1 } { 9 } }$ as rational or irrational.

Simplify the expression $\sqrt { x } - \sqrt { 16 x }$ .

Given $f ( x )$ below, evaluate $f ( 4 - \sqrt { 2 } )$ . $f ( x ) = x ^ { 2 } - 9 x + 5$