Question 1

$-\sqrt{75}$

Accepted Answer

A)  5 
B)  8 
C)  $-5 \sqrt{3}$ 
D)  $-25 \sqrt{3}$ 
A)  5 
B)  8 
C)  $-5 \sqrt{3}$ 
D)  $-25 \sqrt{3}$

Question 2

What is the simplest radical expression that can be multiplied by the given radical expression so that the product can be simplified to no longer contain a radical?
-$\sqrt{\mathrm{xy}^{9} \mathrm{z}^{17}}$

Accepted Answer

A)  $\sqrt{\mathrm{x}}$ 
B)  $\sqrt{x^{3} y z}$ 
C)  $\sqrt{\mathrm{yz}}$ 
D)  $\sqrt{\mathrm{xyz}}$ 
A)  $\sqrt{\mathrm{x}}$ 
B)  $\sqrt{x^{3} y z}$ 
C)  $\sqrt{\mathrm{yz}}$ 
D)  $\sqrt{\mathrm{xyz}}$

Question 3

Simplify the expression. Assume all variables represent nonnegative real numbers.
-$y^{1 / 2} \cdot y^{2 / 3} \cdot y^{4 / 5}$

Accepted Answer

A)  $\mathrm{y}^{30 / 59}$ 
B)  $y^{4 / 15}$ 
C)  $y^{59 / 30}$ 
D)  $\mathrm{y}^{1 / 4}$ 
A)  $\mathrm{y}^{30 / 59}$ 
B)  $y^{4 / 15}$ 
C)  $y^{59 / 30}$ 
D)  $\mathrm{y}^{1 / 4}$

Question 4

Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. The easiest way to simplify the expression $3 \sqrt{\frac{9}{10}}$ is to multiply both the numerator and denominator of $\frac{\sqrt[3]{9}}{\sqrt[3]{10}}$ by $\sqrt[3]{10}$.

Accepted Answer

The statement is false. The easiest way

Question 5

Choose the one alternative that best completes the statement or answers thequestion.
Express in terms of i.
-$\sqrt{-16}$

Accepted Answer

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

Question 6

Add or subtract. Assume all variables represent nonnegative real numbers.

-$11 \sqrt[4]{\mathrm{x}^{7}}-5 \mathrm{x} \sqrt[4]{\mathrm{x}^{3}}$

Accepted Answer

A)  $11 \sqrt[4]{x^{7}}-5 x \sqrt[4]{x^{3}}$ 
B)  $16 \sqrt[4]{x^{3}}$ 
C)  $6 x \sqrt[4]{x^{3}}$ 
D)  $6 x \sqrt[4]{x^{7}}$ 
A)  $11 \sqrt[4]{x^{7}}-5 x \sqrt[4]{x^{3}}$ 
B)  $16 \sqrt[4]{x^{3}}$ 
C)  $6 x \sqrt[4]{x^{3}}$ 
D)  $6 x \sqrt[4]{x^{7}}$

Question 7

Approximate to the nearest thousandth, using a calculator
-$\sqrt{0.000113}$

Accepted Answer

A)  0.011 
B)  0.001 
C)  1.100 
D)  0.110 
A)  0.011 
B)  0.001 
C)  1.100 
D)  0.110

Question 8

Simplify the expression. Assume all variables represent nonnegative real numbers.
-$\sqrt[3]{6} \cdot \sqrt[5]{5}$

Accepted Answer

A)  $\sqrt[15]{972,000}$ 
B)  $\sqrt[15]{30}$ 
C)  $\sqrt[15]{7901}$ 
D)  $\sqrt[8]{972,000}$ 
A)  $\sqrt[15]{972,000}$ 
B)  $\sqrt[15]{30}$ 
C)  $\sqrt[15]{7901}$ 
D)  $\sqrt[8]{972,000}$

Question 9

Solve. Check for extraneous solutions.
-$x^{1 / 3}-1=5$

Accepted Answer

A)  $\{216\}$ 
B)  $\{125\}$ 
C)  $\{\sqrt[3]{6}\}$ 
D)  $\{36\}$ 
A)  $\{216\}$ 
B)  $\{125\}$ 
C)  $\{\sqrt[3]{6}\}$ 
D)  $\{36\}$

Question 10

Explain how to evaluate $(-27)^{2 / 3}$.

Accepted Answer

Answers may vary. One possibil

Question 11

A ssume all variables represent nonnegative real numbers.
-$2 \sqrt{3 \mathrm{x}}(\sqrt{11}+\sqrt{3 \mathrm{x}})$

Accepted Answer

A)  $2 \sqrt{11}+3 x$ 
B)  $6 \sqrt{11 x}+6 x$ 
C)  $2 \sqrt{33 x}+6 x$ 
D)  $2 \sqrt{33}+3 x$ 
A)  $2 \sqrt{11}+3 x$ 
B)  $6 \sqrt{11 x}+6 x$ 
C)  $2 \sqrt{33 x}+6 x$ 
D)  $2 \sqrt{33}+3 x$

Question 12

olve. Check for extraneous solutions.
-$\sqrt{\mathrm{x}+1}=4$

Accepted Answer

A)  $\{15\}$ 
B)  $\{17\}$ 
C)  $\{16\}$ 
D)  $\{25\}$ 
A)  $\{15\}$ 
B)  $\{17\}$ 
C)  $\{16\}$ 
D)  $\{25\}$

Question 13

$\mathrm{i}^{19}{ }_{-} \mathrm{i}^{13}$

Accepted Answer

A)  -2 
B)  - 2i 
C)  0 
D)  $2 \mathrm{i}$ 
A)  -2 
B)  - 2i 
C)  0 
D)  $2 \mathrm{i}$

Question 14

What is the simplest radical expression that can be multiplied by the given radical expression so that the product can be simplified to no longer contain a radical?
-$\sqrt{45}$

Accepted Answer

A)  $\sqrt{7}$ 
B)  $\sqrt{3}$ 
C)  $\sqrt{5}$ 
D)  $\sqrt{9}$ 
A)  $\sqrt{7}$ 
B)  $\sqrt{3}$ 
C)  $\sqrt{5}$ 
D)  $\sqrt{9}$

Question 15

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers.
-$(\sqrt[9]{b})^{7}$

Accepted Answer

A)  $b^{7 / 9}$ 
B)  $b^{-9 / 7}$ 
C)  $b^{-7 / 9}$ 
D)  $b^{9 / 7}$ 
A)  $b^{7 / 9}$ 
B)  $b^{-9 / 7}$ 
C)  $b^{-7 / 9}$ 
D)  $b^{9 / 7}$

Question 16

Solve. Check for extraneous solutions.
-$\sqrt{9 \mathrm{x}-2}=\sqrt{6 \mathrm{x}+9}$

Accepted Answer

A)  $\left\{\frac{3}{11}\right\}$ 
B)  $\left\{\frac{7}{3}\right\}$ 
C)  $\left\{\frac{11}{3}\right\}$ 
D)  $\left\{\frac{11}{15}\right\}$ 
A)  $\left\{\frac{3}{11}\right\}$ 
B)  $\left\{\frac{7}{3}\right\}$ 
C)  $\left\{\frac{11}{3}\right\}$ 
D)  $\left\{\frac{11}{15}\right\}$

Question 17

Add or subtract the complex numbers
-$7 i+(-5-i)$

Accepted Answer

A)  $-5+6 i$ 
B)  $5-6 i$ 
C)  $-5+8 \mathrm{i}$ 
D)  5 - $8 \mathrm{i}$ 
A)  $-5+6 i$ 
B)  $5-6 i$ 
C)  $-5+8 \mathrm{i}$ 
D)  5 - $8 \mathrm{i}$

Question 18

Approximate to the nearest thousandth, using a calculator
-$\sqrt{1.09}$

Accepted Answer

A)  1.000 
B)  1.044 
C)  1.059 
D)  1.031 
A)  1.000 
B)  1.044 
C)  1.059 
D)  1.031

Question 19

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers.
-$(-36)^{1 / 2}$

Accepted Answer

A)  6 
B)  -3 
C)  -6 
D)  Not a real number 
A)  6 
B)  -3 
C)  -6 
D)  Not a real number

Question 20

$(2+7 \mathrm{i}) \div(5+3 \mathrm{i})$

Accepted Answer

A)  $\frac{31}{16}-\frac{29}{16} \mathrm{i}$ 
B)  $\frac{31}{34}+\frac{29}{34} \mathrm{i}$ 
C)  $-\frac{11}{34}-\frac{41}{34} \mathrm{i}$ 
D)  $-\frac{11}{16}-\frac{29}{16} \mathrm{i}$ 
A)  $\frac{31}{16}-\frac{29}{16} \mathrm{i}$ 
B)  $\frac{31}{34}+\frac{29}{34} \mathrm{i}$ 
C)  $-\frac{11}{34}-\frac{41}{34} \mathrm{i}$ 
D)  $-\frac{11}{16}-\frac{29}{16} \mathrm{i}$

$-\sqrt{75}$

What is the simplest radical expression that can be multiplied by the given radical expression so that the product can be simplified to no longer contain a radical? - $\sqrt{\mathrm{xy}^{9} \mathrm{z}^{17}}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $y^{1 / 2} \cdot y^{2 / 3} \cdot y^{4 / 5}$

Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. The easiest way to simplify the expression $3 \sqrt{\frac{9}{10}}$ is to multiply both the numerator and denominator of $\frac{\sqrt[3]{9}}{\sqrt[3]{10}}$ by $\sqrt[3]{10}$ .

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - $\sqrt{-16}$

Add or subtract. Assume all variables represent nonnegative real numbers. - $11 \sqrt[4]{\mathrm{x}^{7}}-5 \mathrm{x} \sqrt[4]{\mathrm{x}^{3}}$

Approximate to the nearest thousandth, using a calculator - $\sqrt{0.000113}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\sqrt[3]{6} \cdot \sqrt[5]{5}$

Solve. Check for extraneous solutions. - $x^{1 / 3}-1=5$

Explain how to evaluate $(-27)^{2 / 3}$ .

A ssume all variables represent nonnegative real numbers. - $2 \sqrt{3 \mathrm{x}}(\sqrt{11}+\sqrt{3 \mathrm{x}})$

olve. Check for extraneous solutions. - $\sqrt{\mathrm{x}+1}=4$

$\mathrm{i}^{19}{ }_{-} \mathrm{i}^{13}$

What is the simplest radical expression that can be multiplied by the given radical expression so that the product can be simplified to no longer contain a radical? - $\sqrt{45}$

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - $(\sqrt[9]{b})^{7}$

Solve. Check for extraneous solutions. - $\sqrt{9 \mathrm{x}-2}=\sqrt{6 \mathrm{x}+9}$

Add or subtract the complex numbers - $7 i+(-5-i)$

Approximate to the nearest thousandth, using a calculator - $\sqrt{1.09}$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $(-36)^{1 / 2}$

$(2+7 \mathrm{i}) \div(5+3 \mathrm{i})$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 7: Radical Expressions and Equations

−75-\sqrt{75}−75​

What is the simplest radical expression that can be multiplied by the given radical expression so that the product can be simplified to no longer contain a radical? - xy9z17\sqrt{\mathrm{xy}^{9} \mathrm{z}^{17}}xy9z17​

Simplify the expression. Assume all variables represent nonnegative real numbers. - y1/2⋅y2/3⋅y4/5y^{1 / 2} \cdot y^{2 / 3} \cdot y^{4 / 5}y1/2⋅y2/3⋅y4/5

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - −16\sqrt{-16}−16​

Add or subtract. Assume all variables represent nonnegative real numbers. - 11x74−5xx3411 \sqrt[4]{\mathrm{x}^{7}}-5 \mathrm{x} \sqrt[4]{\mathrm{x}^{3}}114x7​−5x4x3​

Approximate to the nearest thousandth, using a calculator - 0.000113\sqrt{0.000113}0.000113​

Simplify the expression. Assume all variables represent nonnegative real numbers. - 63⋅55\sqrt[3]{6} \cdot \sqrt[5]{5}36​⋅55​

Solve. Check for extraneous solutions. - x1/3−1=5x^{1 / 3}-1=5x1/3−1=5

Explain how to evaluate (−27)2/3(-27)^{2 / 3}(−27)2/3 .

A ssume all variables represent nonnegative real numbers. - 23x(11+3x)2 \sqrt{3 \mathrm{x}}(\sqrt{11}+\sqrt{3 \mathrm{x}})23x​(11​+3x​)

olve. Check for extraneous solutions. - x+1=4\sqrt{\mathrm{x}+1}=4x+1​=4

i19−i13\mathrm{i}^{19}{ }_{-} \mathrm{i}^{13}i19−​i13

What is the simplest radical expression that can be multiplied by the given radical expression so that the product can be simplified to no longer contain a radical? - 45\sqrt{45}45​

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - (b9)7(\sqrt[9]{b})^{7}(9b​)7

Solve. Check for extraneous solutions. - 9x−2=6x+9\sqrt{9 \mathrm{x}-2}=\sqrt{6 \mathrm{x}+9}9x−2​=6x+9​

Add or subtract the complex numbers - 7i+(−5−i)7 i+(-5-i)7i+(−5−i)

Approximate to the nearest thousandth, using a calculator - 1.09\sqrt{1.09}1.09​

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - (−36)1/2(-36)^{1 / 2}(−36)1/2

(2+7i)÷(5+3i)(2+7 \mathrm{i}) \div(5+3 \mathrm{i})(2+7i)÷(5+3i)

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

$-\sqrt{75}$

What is the simplest radical expression that can be multiplied by the given radical expression so that the product can be simplified to no longer contain a radical? - $\sqrt{\mathrm{xy}^{9} \mathrm{z}^{17}}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $y^{1 / 2} \cdot y^{2 / 3} \cdot y^{4 / 5}$

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - $\sqrt{-16}$

Add or subtract. Assume all variables represent nonnegative real numbers. - $11 \sqrt[4]{\mathrm{x}^{7}}-5 \mathrm{x} \sqrt[4]{\mathrm{x}^{3}}$

Approximate to the nearest thousandth, using a calculator - $\sqrt{0.000113}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\sqrt[3]{6} \cdot \sqrt[5]{5}$

Solve. Check for extraneous solutions. - $x^{1 / 3}-1=5$

Explain how to evaluate $(-27)^{2 / 3}$ .

A ssume all variables represent nonnegative real numbers. - $2 \sqrt{3 \mathrm{x}}(\sqrt{11}+\sqrt{3 \mathrm{x}})$

olve. Check for extraneous solutions. - $\sqrt{\mathrm{x}+1}=4$

$\mathrm{i}^{19}{ }_{-} \mathrm{i}^{13}$

What is the simplest radical expression that can be multiplied by the given radical expression so that the product can be simplified to no longer contain a radical? - $\sqrt{45}$

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - $(\sqrt[9]{b})^{7}$

Solve. Check for extraneous solutions. - $\sqrt{9 \mathrm{x}-2}=\sqrt{6 \mathrm{x}+9}$

Add or subtract the complex numbers - $7 i+(-5-i)$

Approximate to the nearest thousandth, using a calculator - $\sqrt{1.09}$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $(-36)^{1 / 2}$

$(2+7 \mathrm{i}) \div(5+3 \mathrm{i})$