Question 1

Choose the one alternative that best completes the statement or answers thequestion.
Express in terms of i.
-$\sqrt{-147}$

Accepted Answer

A)  $7 \sqrt{3} \mathrm{i}$ 
B)  $-7 \sqrt{3} i$ 
C)  $7 \sqrt{3}$ 
D)  $-7 \sqrt{3}$ 
A)  $7 \sqrt{3} \mathrm{i}$ 
B)  $-7 \sqrt{3} i$ 
C)  $7 \sqrt{3}$ 
D)  $-7 \sqrt{3}$

Question 2

Find the domain of the function. Express the answer in interval notation.
-$f(x)=\sqrt{9-2 x}$

Accepted Answer

A)  $\left[\frac{9}{2}, \infty\right)$ 
B)  $\left[-\infty, \frac{9}{2}\right]$ 
C)  $\left[-\frac{9}{2}, \infty\right)$ 
D)  $\left(-\infty, \frac{9}{2}\right)$ 
A)  $\left[\frac{9}{2}, \infty\right)$ 
B)  $\left[-\infty, \frac{9}{2}\right]$ 
C)  $\left[-\frac{9}{2}, \infty\right)$ 
D)  $\left(-\infty, \frac{9}{2}\right)$

Question 3

Simplify by rationalizing the denominator. Write your answer in a + bi form.
-$\frac{7}{3 i}$

Accepted Answer

A)  $-\frac{3}{7} \mathrm{i}$ 
B)  $\frac{7}{3} \mathrm{i}$ 
C)  $-\frac{7}{3} \mathrm{i}$ 
D)  $\frac{3}{7} \mathrm{i}$ 
A)  $-\frac{3}{7} \mathrm{i}$ 
B)  $\frac{7}{3} \mathrm{i}$ 
C)  $-\frac{7}{3} \mathrm{i}$ 
D)  $\frac{3}{7} \mathrm{i}$

Question 4

Solve. Check for extraneous solutions.
-$(2 x-20)^{1 / 4}+5=15$

Accepted Answer

A)  $\{10\}$ 
B)  $\{5010\}$ 
C)  $\{10,020\}$ 
D)  $\{30\}$ 
A)  $\{10\}$ 
B)  $\{5010\}$ 
C)  $\{10,020\}$ 
D)  $\{30\}$

Question 5

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$\sqrt{18 k^{7} q^{8}}$

Accepted Answer

A)  $3 k^{3} q^{4} \sqrt{2}$ 
B)  $3 k^{3} q^{4} \sqrt{2 k}$ 
C)  $3 k^{7} q^{8} \sqrt{2 k}$ 
D)  $3 k^{2} q^{4} \sqrt{2 k}$ 
A)  $3 k^{3} q^{4} \sqrt{2}$ 
B)  $3 k^{3} q^{4} \sqrt{2 k}$ 
C)  $3 k^{7} q^{8} \sqrt{2 k}$ 
D)  $3 k^{2} q^{4} \sqrt{2 k}$

Question 6

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers.
-$\left(b^{7}\right)^{2 / 7}$

Accepted Answer

A)  $b^{2 / 49}$ 
B)  $b^{9 / 7}$ 
C)  $b^{1 / 7}$ 
D)  $b^{2}$ 
A)  $b^{2 / 49}$ 
B)  $b^{9 / 7}$ 
C)  $b^{1 / 7}$ 
D)  $b^{2}$

Question 7

Choose the one alternative that best completes the statement or answers thequestion.
Express in terms of i.
-$-\sqrt{-224}$

Accepted Answer

A)  $4 \sqrt{14} i$ 
B)  $-4 \sqrt{14} i$ 
C)  $4 \sqrt{14}$ 
D)  $-4 \sqrt{14}$ 
A)  $4 \sqrt{14} i$ 
B)  $-4 \sqrt{14} i$ 
C)  $4 \sqrt{14}$ 
D)  $-4 \sqrt{14}$

Question 8

Approximate to the nearest thousandth, using a calculator
-$-\sqrt{77}$

Accepted Answer

A)  -8.772 
B)  -8.780 
C)  -77.000 
D)  -8.775 
A)  -8.772 
B)  -8.780 
C)  -77.000 
D)  -8.775

Question 9

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers.
-$\sqrt{\frac{18 \mathrm{x}^{3}}{\mathrm{y} 5}}$

Accepted Answer

A)  $\frac{3 x}{y 2} \sqrt{\frac{2 x}{y}}$ 
B)  $\frac{x \sqrt{18 x y}}{y 3}$ 
C)  $\frac{3 x \sqrt{2 x y}}{y 3}$ 
D)  $\frac{3 x^{3} \sqrt{2}}{y 5}$ 
A)  $\frac{3 x}{y 2} \sqrt{\frac{2 x}{y}}$ 
B)  $\frac{x \sqrt{18 x y}}{y 3}$ 
C)  $\frac{3 x \sqrt{2 x y}}{y 3}$ 
D)  $\frac{3 x^{3} \sqrt{2}}{y 5}$

Question 10

Does the equation $\sqrt{\mathrm{x}+2}=-\sqrt{\mathrm{x}}$ have a real- number solution? Explain.

Accepted Answer

No. Since neither radical can have a val

Question 11

Solve. Check for extraneous solutions.
-$\sqrt{\mathrm{x}+7}+5=\mathrm{x}$

Accepted Answer

A)  $\{2\}$ 
B)  $\{2,9\}$ 
C)  $\{9,18\}$ 
D)  $\{9\}$ 
A)  $\{2\}$ 
B)  $\{2,9\}$ 
C)  $\{9,18\}$ 
D)  $\{9\}$

Question 12

i8

Accepted Answer

A)  1 
B)  - i 
C)  $\mathrm{i}$ 
D)  - 1 
A)  1 
B)  - i 
C)  $\mathrm{i}$ 
D)  - 1

Question 13

Simplify. Assume all variables represent nonnegative values.
-$\sqrt{\frac{48 x^{2} y}{49}}$

Accepted Answer

A)  $\frac{4 \sqrt{3 x^{2} y}}{7}$ 
B)  $\frac{4 x \sqrt{3 y}}{7}$ 
C)  $16 x \sqrt{3 y}$ 
D)  $x \sqrt{\frac{48 y}{7}}$ 
A)  $\frac{4 \sqrt{3 x^{2} y}}{7}$ 
B)  $\frac{4 x \sqrt{3 y}}{7}$ 
C)  $16 x \sqrt{3 y}$ 
D)  $x \sqrt{\frac{48 y}{7}}$

Question 14

Solve. Check for extraneous solutions.
-$\sqrt{10+\mathrm{x}}+\sqrt{11-5 \mathrm{x}}=-1$

Accepted Answer

A)  $\left\{\frac{11}{2}\right\}$ 
B)  $\{1\}$ 
C)  $\{0\}$ 
D)  $\varnothing$ 
A)  $\left\{\frac{11}{2}\right\}$ 
B)  $\{1\}$ 
C)  $\{0\}$ 
D)  $\varnothing$

Question 15

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers.
-$\left(x^{4} y^{6}\right)^{1 / 2}$

Accepted Answer

A)  $x^{2} y^{3}$ 
B)  $2 x^{4} y^{6}$ 
C)  $x^{8} y^{12}$ 
D)  $x^{3} y^{2}$ 
A)  $x^{2} y^{3}$ 
B)  $2 x^{4} y^{6}$ 
C)  $x^{8} y^{12}$ 
D)  $x^{3} y^{2}$

Question 16

Find the missing complex number
-$(2-3 \mathrm{i})(?)=9+4 \mathrm{i}$

Accepted Answer

A)  $\frac{30}{13}+\frac{19}{13} \mathrm{i}$ 
B)  $\frac{6}{13}+\frac{35}{13} \mathrm{i}$ 
C)  $-6+7 i$ 
D)  $-\frac{6}{5}+7 \mathrm{i}$ 
A)  $\frac{30}{13}+\frac{19}{13} \mathrm{i}$ 
B)  $\frac{6}{13}+\frac{35}{13} \mathrm{i}$ 
C)  $-6+7 i$ 
D)  $-\frac{6}{5}+7 \mathrm{i}$

Question 17

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers.
-$\sqrt[2]{x^{5} y^{7}}$

Accepted Answer

A)  $\left(x^{5} y z^{7}\right)^{1 / 2}$ 
B)  $x^{3} y^{-1} z^{5}$ 
C)  $\left(x^{5} y z^{7}\right)^{2}$ 
D)  $\left(x^{5} y z^{7}\right)^{-2}$ 
A)  $\left(x^{5} y z^{7}\right)^{1 / 2}$ 
B)  $x^{3} y^{-1} z^{5}$ 
C)  $\left(x^{5} y z^{7}\right)^{2}$ 
D)  $\left(x^{5} y z^{7}\right)^{-2}$

Question 18

A manufacturer's cost is given by $C=200 \sqrt[3]{n}+200$, where $C$ is the cost and $n$ is the number of parts produced. How many parts are produced when the cost is $\$ 3600$ ?

Accepted Answer

A)  39,304 
B)  289 
C)  3400 
D)  4913 
A)  39,304 
B)  289 
C)  3400 
D)  4913

Question 19

Rationalize the denominator and simplify.
-$\frac{\sqrt{2}}{\sqrt{7}+5}$

Accepted Answer

A)  $\frac{\sqrt{14}+5 \sqrt{2}}{-18}$ 
B)  $\frac{\sqrt{14}-5 \sqrt{2}}{12}$ 
C)  $\frac{3 \sqrt{14}+7 \sqrt{2}}{35}$ 
D)  $\frac{\sqrt{14}-5 \sqrt{2}}{-18}$ 
A)  $\frac{\sqrt{14}+5 \sqrt{2}}{-18}$ 
B)  $\frac{\sqrt{14}-5 \sqrt{2}}{12}$ 
C)  $\frac{3 \sqrt{14}+7 \sqrt{2}}{35}$ 
D)  $\frac{\sqrt{14}-5 \sqrt{2}}{-18}$

Question 20

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

-$8 \sqrt[4]{m^{9} p^{6}}-6 m^{2} p \sqrt[4]{m p^{2}}$

Accepted Answer

A)  $2 m^{2} p \sqrt[4]{m p^{2}}$ 
B)  $14 m^{2} p \sqrt[4]{m p^{2}}$ 
C)  2 
D)  Cannot simplify 
A)  $2 m^{2} p \sqrt[4]{m p^{2}}$ 
B)  $14 m^{2} p \sqrt[4]{m p^{2}}$ 
C)  2 
D)  Cannot simplify

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - $\sqrt{-147}$

Find the domain of the function. Express the answer in interval notation. - $f(x)=\sqrt{9-2 x}$

Simplify by rationalizing the denominator. Write your answer in a + bi form. - $\frac{7}{3 i}$

Solve. Check for extraneous solutions. - $(2 x-20)^{1 / 4}+5=15$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt{18 k^{7} q^{8}}$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $\left(b^{7}\right)^{2 / 7}$

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - $-\sqrt{-224}$

Approximate to the nearest thousandth, using a calculator - $-\sqrt{77}$

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - $\sqrt{\frac{18 \mathrm{x}^{3}}{\mathrm{y} 5}}$

Does the equation $\sqrt{\mathrm{x}+2}=-\sqrt{\mathrm{x}}$ have a real- number solution? Explain.

Solve. Check for extraneous solutions. - $\sqrt{\mathrm{x}+7}+5=\mathrm{x}$

i8

Simplify. Assume all variables represent nonnegative values. - $\sqrt{\frac{48 x^{2} y}{49}}$

Solve. Check for extraneous solutions. - $\sqrt{10+\mathrm{x}}+\sqrt{11-5 \mathrm{x}}=-1$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $\left(x^{4} y^{6}\right)^{1 / 2}$

Find the missing complex number - $(2-3 \mathrm{i})(?)=9+4 \mathrm{i}$

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - $\sqrt[2]{x^{5} y^{7}}$

A manufacturer's cost is given by $C=200 \sqrt[3]{n}+200$ , where $C$ is the cost and $n$ is the number of parts produced. How many parts are produced when the cost is $\$ 3600$ ?

Rationalize the denominator and simplify. - $\frac{\sqrt{2}}{\sqrt{7}+5}$

Add or subtract. Assume all variables represent nonnegative real numbers. - $8 \sqrt[4]{m^{9} p^{6}}-6 m^{2} p \sqrt[4]{m p^{2}}$

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

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - −147\sqrt{-147}−147​

Find the domain of the function. Express the answer in interval notation. - f(x)=9−2xf(x)=\sqrt{9-2 x}f(x)=9−2x​

Simplify by rationalizing the denominator. Write your answer in a + bi form. - 73i\frac{7}{3 i}3i7​

Solve. Check for extraneous solutions. - (2x−20)1/4+5=15(2 x-20)^{1 / 4}+5=15(2x−20)1/4+5=15

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - 18k7q8\sqrt{18 k^{7} q^{8}}18k7q8​

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - (b7)2/7\left(b^{7}\right)^{2 / 7}(b7)2/7

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - −−224-\sqrt{-224}−−224​

Approximate to the nearest thousandth, using a calculator - −77-\sqrt{77}−77​

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - 18x3y5\sqrt{\frac{18 \mathrm{x}^{3}}{\mathrm{y} 5}}y518x3​​

Does the equation x+2=−x\sqrt{\mathrm{x}+2}=-\sqrt{\mathrm{x}}x+2​=−x​ have a real- number solution? Explain.

Solve. Check for extraneous solutions. - x+7+5=x\sqrt{\mathrm{x}+7}+5=\mathrm{x}x+7​+5=x

i8

Simplify. Assume all variables represent nonnegative values. - 48x2y49\sqrt{\frac{48 x^{2} y}{49}}4948x2y​​

Solve. Check for extraneous solutions. - 10+x+11−5x=−1\sqrt{10+\mathrm{x}}+\sqrt{11-5 \mathrm{x}}=-110+x​+11−5x​=−1

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - (x4y6)1/2\left(x^{4} y^{6}\right)^{1 / 2}(x4y6)1/2

Find the missing complex number - (2−3i)(?)=9+4i(2-3 \mathrm{i})(?)=9+4 \mathrm{i}(2−3i)(?)=9+4i

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - x5y72\sqrt[2]{x^{5} y^{7}}2x5y7​

A manufacturer's cost is given by C=200n3+200C=200 \sqrt[3]{n}+200C=2003n​+200 , where CCC is the cost and nnn is the number of parts produced. How many parts are produced when the cost is $3600\$ 3600$3600 ?

Rationalize the denominator and simplify. - 27+5\frac{\sqrt{2}}{\sqrt{7}+5}7​+52​​

Add or subtract. Assume all variables represent nonnegative real numbers. - 8m9p64−6m2pmp248 \sqrt[4]{m^{9} p^{6}}-6 m^{2} p \sqrt[4]{m p^{2}}84m9p6​−6m2p4mp2​

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

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - $\sqrt{-147}$

Find the domain of the function. Express the answer in interval notation. - $f(x)=\sqrt{9-2 x}$

Simplify by rationalizing the denominator. Write your answer in a + bi form. - $\frac{7}{3 i}$

Solve. Check for extraneous solutions. - $(2 x-20)^{1 / 4}+5=15$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt{18 k^{7} q^{8}}$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $\left(b^{7}\right)^{2 / 7}$

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - $-\sqrt{-224}$

Approximate to the nearest thousandth, using a calculator - $-\sqrt{77}$

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - $\sqrt{\frac{18 \mathrm{x}^{3}}{\mathrm{y} 5}}$

Does the equation $\sqrt{\mathrm{x}+2}=-\sqrt{\mathrm{x}}$ have a real- number solution? Explain.

Solve. Check for extraneous solutions. - $\sqrt{\mathrm{x}+7}+5=\mathrm{x}$

Simplify. Assume all variables represent nonnegative values. - $\sqrt{\frac{48 x^{2} y}{49}}$

Solve. Check for extraneous solutions. - $\sqrt{10+\mathrm{x}}+\sqrt{11-5 \mathrm{x}}=-1$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $\left(x^{4} y^{6}\right)^{1 / 2}$

Find the missing complex number - $(2-3 \mathrm{i})(?)=9+4 \mathrm{i}$

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - $\sqrt[2]{x^{5} y^{7}}$

A manufacturer's cost is given by $C=200 \sqrt[3]{n}+200$ , where $C$ is the cost and $n$ is the number of parts produced. How many parts are produced when the cost is $\$ 3600$ ?

Rationalize the denominator and simplify. - $\frac{\sqrt{2}}{\sqrt{7}+5}$

Add or subtract. Assume all variables represent nonnegative real numbers. - $8 \sqrt[4]{m^{9} p^{6}}-6 m^{2} p \sqrt[4]{m p^{2}}$