Question 1

Write the quotient $\frac { 24 } { 2 i }$ in standard form.

Accepted Answer

A)  $12$ 
B)  $- 12 i$ 
C)  $- \frac { 12 } { i }$ 
D)  $\frac { 12 } { i }$ 
E)  $2$ 
A)  $12$ 
B)  $- 12 i$ 
C)  $- \frac { 12 } { i }$ 
D)  $\frac { 12 } { i }$ 
E)  $2$

Question 2

Simplify the expression $\frac { 5 } { \sqrt { 17 } - 3 }$ .

Accepted Answer

A)  $\frac { 5 ( \sqrt { 17 } + 3 ) } { 280 }$ 
B)  $\frac { 5 ( \sqrt { 17 } - 3 ) } { 26 }$ 
C)  $\frac { 5 ( \sqrt { 17 } + 3 ) } { 26 }$ 
D)  $\frac { 5 ( \sqrt { 17 } + 3 ) } { 8 }$ 
E)  $\frac { 5 ( \sqrt { 17 } - 3 ) } { 8 }$ 
A)  $\frac { 5 ( \sqrt { 17 } + 3 ) } { 280 }$ 
B)  $\frac { 5 ( \sqrt { 17 } - 3 ) } { 26 }$ 
C)  $\frac { 5 ( \sqrt { 17 } + 3 ) } { 26 }$ 
D)  $\frac { 5 ( \sqrt { 17 } + 3 ) } { 8 }$ 
E)  $\frac { 5 ( \sqrt { 17 } - 3 ) } { 8 }$

Question 3

Find all of the cube roots of the perfect cube $\frac { 216 } { 125 }$ .

Accepted Answer

A)  $\frac { 31 } { 18 }$ 
B)  $\frac { 215 } { 124 }$ 
C)  $\frac { 6 } { 5 }$ 
D)  $ \frac{5}{6} $ 
E)  $\frac { 36 } { 25 }$ 
A)  $\frac { 31 } { 18 }$ 
B)  $\frac { 215 } { 124 }$ 
C)  $\frac { 6 } { 5 }$ 
D)  $ \frac{5}{6} $ 
E)  $\frac { 36 } { 25 }$

Question 4

Perform the operation and write the result in standard form. $$( 2 i ) ^ { 2 }$$

Accepted Answer

A)  $- 2 i$ 
B)  $- 4$ 
C)  $- 4 i$ 
D)  $4 i$ 
E)  $2$ 
A)  $- 2 i$ 
B)  $- 4$ 
C)  $- 4 i$ 
D)  $4 i$ 
E)  $2$

Question 5

Find the dimensions of a piece of carpet for a square classroom with $559$ square feet of floor space. Round your answer to two decimal places.

Accepted Answer

A)  $23.64 \text { square feet }$ 
B)  $23.64 \text { feet } \times 23.64 \text { feet }$ 
C)  $23.64 \text { feet } \times 312,481 \text { feet }$ 
D)  $312,481 \text { feet } \times 312,481 \text { feet }$ 
E)  $23.64 \text { feet } \times 2 \text { feet }$ 
A)  $23.64 \text { square feet }$ 
B)  $23.64 \text { feet } \times 23.64 \text { feet }$ 
C)  $23.64 \text { feet } \times 312,481 \text { feet }$ 
D)  $312,481 \text { feet } \times 312,481 \text { feet }$ 
E)  $23.64 \text { feet } \times 2 \text { feet }$

Question 6

Solve $x = \sqrt { 44 - 7 x }$ , if possible.

Accepted Answer

A)  x=-4 
B)  x=7 
C)  x=4 
D)  x=44 
E) no solution 
A)  x=-4 
B)  x=7 
C)  x=4 
D)  x=44 
E) no solution

Question 7

Simplify the expression $9 \sqrt { u } - 3 + \sqrt { u } + 8$.

Accepted Answer

A)  $10 \sqrt { u } + 5$ 
B)  $\sqrt { u } + 5$ 
C)  $5 \sqrt { u } + 10$ 
D)  $10 \sqrt { u } - 5$ 
E)  $10 \sqrt { u }$ 
A)  $10 \sqrt { u } + 5$ 
B)  $\sqrt { u } + 5$ 
C)  $5 \sqrt { u } + 10$ 
D)  $10 \sqrt { u } - 5$ 
E)  $10 \sqrt { u }$

Question 8

For $f ( x ) = \sqrt { x } - \sqrt { x - 169 }$ , find x such that $f ( x ) = 1$ .

Accepted Answer

A)  14,450 
B)  14,112 
C)  28,900 
D)  7,056 
E)  $7,225$ 
A)  14,450 
B)  14,112 
C)  28,900 
D)  7,056 
E)  $7,225$

Question 9

Simplify the radical $\sqrt { 27 }$ , if possible.

Accepted Answer

A)  $9 \sqrt { 3 }$ 
B)  27 
C)  $\sqrt { 3 }$ 
D)  $3 \sqrt { 3 }$ 
E) cannot be simplified 
A)  $9 \sqrt { 3 }$ 
B)  27 
C)  $\sqrt { 3 }$ 
D)  $3 \sqrt { 3 }$ 
E) cannot be simplified

Question 10

Perform the operation and write the result in standard form. $\sqrt { - 28 } + \sqrt { - 112 }$

Accepted Answer

A)  $9 i \sqrt { 7 }$ 
B)  $\sqrt { 11 } i \sqrt { 7 }$ 
C)  $- 5 i \sqrt { 7 }$ 
D)  $6 i \sqrt { 7 }$ 
E)  $- 2 i \sqrt { 7 }$ 
A)  $9 i \sqrt { 7 }$ 
B)  $\sqrt { 11 } i \sqrt { 7 }$ 
C)  $- 5 i \sqrt { 7 }$ 
D)  $6 i \sqrt { 7 }$ 
E)  $- 2 i \sqrt { 7 }$

Question 11

Find the principal square root of $\sqrt { - 25 }$ , if possible. Do not use a calculator.

Accepted Answer

A) 5 
B)  25,-25 
C)  -5 
D)  $\sqrt { 5 } , - \sqrt { 5 }$ 
E) no real roots 
A) 5 
B)  25,-25 
C)  -5 
D)  $\sqrt { 5 } , - \sqrt { 5 }$ 
E) no real roots

Question 12

Find the multiplicative inverse of the complex number $5 + 6 i$ .

Accepted Answer

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

Question 13

Multiply and simplify. $( \sqrt { 13 } + 5 ) ( \sqrt { 5 } - 13 )$

Accepted Answer

A)  $\sqrt { 65 } - 5 \sqrt { 5 } + 13 \sqrt { 13 } - 65$ 
B)  $\sqrt { 65 } + 13 \sqrt { 5 } + 5 \sqrt { 13 } - 65$ 
C)  $\sqrt { 65 } + 13 \sqrt { 13 } + 5 \sqrt { 5 } - 65$ 
D)  $\sqrt { 65 } + 13 \sqrt { 5 } - 5 \sqrt { 13 } - 65$ 
E)  $\sqrt { 65 } - 13 \sqrt { 13 } + 5 \sqrt { 5 } - 65$ 
A)  $\sqrt { 65 } - 5 \sqrt { 5 } + 13 \sqrt { 13 } - 65$ 
B)  $\sqrt { 65 } + 13 \sqrt { 5 } + 5 \sqrt { 13 } - 65$ 
C)  $\sqrt { 65 } + 13 \sqrt { 13 } + 5 \sqrt { 5 } - 65$ 
D)  $\sqrt { 65 } + 13 \sqrt { 5 } - 5 \sqrt { 13 } - 65$ 
E)  $\sqrt { 65 } - 13 \sqrt { 13 } + 5 \sqrt { 5 } - 65$

Question 14

Evaluate the radical expression $\sqrt { - 12 }$ without using a calculator. If not possible, state the reason.

Accepted Answer

A)  -12 
B)  -144 
C)  144 
D)  12 
E) not a real number 
A)  -12 
B)  -144 
C)  144 
D)  12 
E) not a real number

Question 15

Perform the operation and write the result in standard form. $$( 4 + 9 i ) ^ { 2 }$$

Accepted Answer

A)  $16 + 81 i$ 
B)  $97 - 8 i$ 
C)  $- 65 + 72 i$ 
D)  $- 8 + 18 i$ 
E)  $16 - 9 i$ 
A)  $16 + 81 i$ 
B)  $97 - 8 i$ 
C)  $- 65 + 72 i$ 
D)  $- 8 + 18 i$ 
E)  $16 - 9 i$

Question 16

Simplify the expression $\frac { 5 } { \sqrt { 5 } + \sqrt { 7 } }$ .

Accepted Answer

A)  $\frac { 5 ( \sqrt { 5 } + \sqrt { 7 } ) } { 2 }$ 
B)  $\frac { 5 ( \sqrt { 5 } - \sqrt { 7 } ) } { 12 }$ 
C)  $- \frac { 5 ( \sqrt { 5 } - \sqrt { 7 } ) } { 2 }$ 
D)  $\frac { 5 ( \sqrt { 5 } - \sqrt { 7 } ) } { 24 }$ 
E)  $\frac { 5 ( \sqrt { 5 } + \sqrt { 7 } ) } { 74 }$ 
A)  $\frac { 5 ( \sqrt { 5 } + \sqrt { 7 } ) } { 2 }$ 
B)  $\frac { 5 ( \sqrt { 5 } - \sqrt { 7 } ) } { 12 }$ 
C)  $- \frac { 5 ( \sqrt { 5 } - \sqrt { 7 } ) } { 2 }$ 
D)  $\frac { 5 ( \sqrt { 5 } - \sqrt { 7 } ) } { 24 }$ 
E)  $\frac { 5 ( \sqrt { 5 } + \sqrt { 7 } ) } { 74 }$

Question 17

Multiply and simplify the expression $\sqrt { 5 } \sqrt { 21 }$ .

Accepted Answer

A)  105 
B)  $\sqrt { 105 }$ 
C)  $\sqrt { 5 } + \sqrt { 21 }$ 
D)  $\sqrt { 21 }$ 
E)  $\sqrt { 5 }$ 
A)  105 
B)  $\sqrt { 105 }$ 
C)  $\sqrt { 5 } + \sqrt { 21 }$ 
D)  $\sqrt { 21 }$ 
E)  $\sqrt { 5 }$

Question 18

Use a calculator to approximate $\frac { - 14 - 3 \sqrt { 2 } } { 2 }$ . Round your answer to three decimal places.

Accepted Answer

A) -9.121 
B) -18.243 
C) -11.243 
D) -2.121 
E) -7 
A) -9.121 
B) -18.243 
C) -11.243 
D) -2.121 
E) -7

Question 19

Determine which value of x is a solution of $\sqrt { 3 x } - 8 = 0$ .

Accepted Answer

A)  x=64 
B)  x=-8 
C)  x=8 
D)  x=3 
E)  $x = \frac { 64 } { 3 }$ 
A)  x=64 
B)  x=-8 
C)  x=8 
D)  x=3 
E)  $x = \frac { 64 } { 3 }$

Question 20

Rewrite the expression $z ^ { 3 } \sqrt { y ^ { 3 } z ^ { 6 } }$ using rational exponents.

Accepted Answer

A)  $y ^ { 3 } z ^ { 6 }$ 
B)  $y ^ { 3 } z ^ { 3 }$ 
C)  $y ^ { 3 / 2 } z ^ { 4 }$ 
D)  $y ^ { 3 / 2 } z ^ { 6 }$ 
E)  $y ^ { 3 / 2 } z ^ { 3 }$ 
A)  $y ^ { 3 } z ^ { 6 }$ 
B)  $y ^ { 3 } z ^ { 3 }$ 
C)  $y ^ { 3 / 2 } z ^ { 4 }$ 
D)  $y ^ { 3 / 2 } z ^ { 6 }$ 
E)  $y ^ { 3 / 2 } z ^ { 3 }$

Write the quotient $\frac { 24 } { 2 i }$ in standard form.

Simplify the expression $\frac { 5 } { \sqrt { 17 } - 3 }$ .

Find all of the cube roots of the perfect cube $\frac { 216 } { 125 }$ .

Perform the operation and write the result in standard form. $( 2 i ) ^ { 2 }$

Find the dimensions of a piece of carpet for a square classroom with $559$ square feet of floor space. Round your answer to two decimal places.

Solve $x = \sqrt { 44 - 7 x }$ , if possible.

Simplify the expression $9 \sqrt { u } - 3 + \sqrt { u } + 8$ .

For $f ( x ) = \sqrt { x } - \sqrt { x - 169 }$ , find x such that $f ( x ) = 1$ .

Simplify the radical $\sqrt { 27 }$ , if possible.

Perform the operation and write the result in standard form. $\sqrt { - 28 } + \sqrt { - 112 }$

Find the principal square root of $\sqrt { - 25 }$ , if possible. Do not use a calculator.

Find the multiplicative inverse of the complex number $5 + 6 i$ .

Multiply and simplify. $( \sqrt { 13 } + 5 ) ( \sqrt { 5 } - 13 )$

Evaluate the radical expression $\sqrt { - 12 }$ without using a calculator. If not possible, state the reason.

Perform the operation and write the result in standard form. $( 4 + 9 i ) ^ { 2 }$

Simplify the expression $\frac { 5 } { \sqrt { 5 } + \sqrt { 7 } }$ .

Multiply and simplify the expression $\sqrt { 5 } \sqrt { 21 }$ .

Use a calculator to approximate $\frac { - 14 - 3 \sqrt { 2 } } { 2 }$ . Round your answer to three decimal places.

Determine which value of x is a solution of $\sqrt { 3 x } - 8 = 0$ .

Rewrite the expression $z ^ { 3 } \sqrt { y ^ { 3 } z ^ { 6 } }$ using rational exponents.

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

Write the quotient 242i\frac { 24 } { 2 i }2i24​ in standard form.

Simplify the expression 517−3\frac { 5 } { \sqrt { 17 } - 3 }17​−35​ .

Find all of the cube roots of the perfect cube 216125\frac { 216 } { 125 }125216​ .

Perform the operation and write the result in standard form. (2i)2( 2 i ) ^ { 2 }(2i)2

Find the dimensions of a piece of carpet for a square classroom with 559559559 square feet of floor space. Round your answer to two decimal places.

Solve x=44−7xx = \sqrt { 44 - 7 x }x=44−7x​ , if possible.

Simplify the expression 9u−3+u+89 \sqrt { u } - 3 + \sqrt { u } + 89u​−3+u​+8 .

For f(x)=x−x−169f ( x ) = \sqrt { x } - \sqrt { x - 169 }f(x)=x​−x−169​ , find x such that f(x)=1f ( x ) = 1f(x)=1 .

Simplify the radical 27\sqrt { 27 }27​ , if possible.

Perform the operation and write the result in standard form. −28+−112\sqrt { - 28 } + \sqrt { - 112 }−28​+−112​

Find the principal square root of −25\sqrt { - 25 }−25​ , if possible. Do not use a calculator.

Find the multiplicative inverse of the complex number 5+6i5 + 6 i5+6i .

Multiply and simplify. (13+5)(5−13)( \sqrt { 13 } + 5 ) ( \sqrt { 5 } - 13 )(13​+5)(5​−13)

Evaluate the radical expression −12\sqrt { - 12 }−12​ without using a calculator. If not possible, state the reason.

Perform the operation and write the result in standard form. (4+9i)2( 4 + 9 i ) ^ { 2 }(4+9i)2

Simplify the expression 55+7\frac { 5 } { \sqrt { 5 } + \sqrt { 7 } }5​+7​5​ .

Multiply and simplify the expression 521\sqrt { 5 } \sqrt { 21 }5​21​ .

Use a calculator to approximate −14−322\frac { - 14 - 3 \sqrt { 2 } } { 2 }2−14−32​​ . Round your answer to three decimal places.

Determine which value of x is a solution of 3x−8=0\sqrt { 3 x } - 8 = 03x​−8=0 .

Rewrite the expression z3y3z6z ^ { 3 } \sqrt { y ^ { 3 } z ^ { 6 } }z3y3z6​ using rational exponents.

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

Write the quotient $\frac { 24 } { 2 i }$ in standard form.

Simplify the expression $\frac { 5 } { \sqrt { 17 } - 3 }$ .

Find all of the cube roots of the perfect cube $\frac { 216 } { 125 }$ .

Perform the operation and write the result in standard form. $( 2 i ) ^ { 2 }$

Find the dimensions of a piece of carpet for a square classroom with $559$ square feet of floor space. Round your answer to two decimal places.

Solve $x = \sqrt { 44 - 7 x }$ , if possible.

Simplify the expression $9 \sqrt { u } - 3 + \sqrt { u } + 8$ .

For $f ( x ) = \sqrt { x } - \sqrt { x - 169 }$ , find x such that $f ( x ) = 1$ .

Simplify the radical $\sqrt { 27 }$ , if possible.

Perform the operation and write the result in standard form. $\sqrt { - 28 } + \sqrt { - 112 }$

Find the principal square root of $\sqrt { - 25 }$ , if possible. Do not use a calculator.

Find the multiplicative inverse of the complex number $5 + 6 i$ .

Multiply and simplify. $( \sqrt { 13 } + 5 ) ( \sqrt { 5 } - 13 )$

Evaluate the radical expression $\sqrt { - 12 }$ without using a calculator. If not possible, state the reason.

Perform the operation and write the result in standard form. $( 4 + 9 i ) ^ { 2 }$

Simplify the expression $\frac { 5 } { \sqrt { 5 } + \sqrt { 7 } }$ .

Multiply and simplify the expression $\sqrt { 5 } \sqrt { 21 }$ .

Use a calculator to approximate $\frac { - 14 - 3 \sqrt { 2 } } { 2 }$ . Round your answer to three decimal places.

Determine which value of x is a solution of $\sqrt { 3 x } - 8 = 0$ .

Rewrite the expression $z ^ { 3 } \sqrt { y ^ { 3 } z ^ { 6 } }$ using rational exponents.