Question 1

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.
-$\sqrt{u^{32}}$

Accepted Answer

A)  $\sqrt{\mathrm{u}^{16}}$ 
B)  $\sqrt{\mathrm{u}^{32}}$ 
C)  $u^{5.657}$ 
D)  $\mathrm{u}^{16}$ 
A)  $\sqrt{\mathrm{u}^{16}}$ 
B)  $\sqrt{\mathrm{u}^{32}}$ 
C)  $u^{5.657}$ 
D)  $\mathrm{u}^{16}$

Question 2

Write the expression in the form a + bi.
-$\frac{-7+11 \mathrm{i}}{-20 \mathrm{i}}$

Accepted Answer

A)  $\frac{11}{20}-\frac{7}{20} \mathrm{i}$ 
B)  $-\frac{11}{20}+\frac{7}{20} \mathrm{i}$ 
C)  $-\frac{11}{20}-\frac{7}{20} \mathrm{i}$ 
D)  $\frac{11}{20}+\frac{7}{20} \mathrm{i}$ 
A)  $\frac{11}{20}-\frac{7}{20} \mathrm{i}$ 
B)  $-\frac{11}{20}+\frac{7}{20} \mathrm{i}$ 
C)  $-\frac{11}{20}-\frac{7}{20} \mathrm{i}$ 
D)  $\frac{11}{20}+\frac{7}{20} \mathrm{i}$

Question 3

Simplify the expression involving rational exponents.
-$\left(-\frac{64}{125}\right)^{-4 / 3}$

Accepted Answer

A)  $\frac{256}{625}$ 
B)  $-\frac{256}{625}$ 
C)  $\frac{625}{256}$ 
D)  Not a real number 
A)  $\frac{256}{625}$ 
B)  $-\frac{256}{625}$ 
C)  $\frac{625}{256}$ 
D)  Not a real number

Question 4

Express the radical in simplified form.Assume that all variables represent positive real numbers.
-$\sqrt[3]{-64}$

Accepted Answer

A)  -4 
B)  4 
C)  -16 
D)  16 
A)  -4 
B)  4 
C)  -16 
D)  16

Question 5

Choose the one alternative that best completes the statement or answers the question.
Solve the equation
-$\sqrt{9 a-2}-\sqrt{6 a+6}=0$

Accepted Answer

A)  $\left\{\frac{8}{3}\right\}$ 
B)  $\left\{\frac{4}{3}\right\}$ 
C)  $\left\{\frac{3}{8}\right\}$ 
D)  $\left\{\frac{8}{15}\right\}$ 
A)  $\left\{\frac{8}{3}\right\}$ 
B)  $\left\{\frac{4}{3}\right\}$ 
C)  $\left\{\frac{3}{8}\right\}$ 
D)  $\left\{\frac{8}{15}\right\}$

Question 6

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.
-$\frac{x^{1 / 2} \cdot x^{3 / 10} \cdot x^{2 / 5}}{\left(x^{2}\right)^{-1 / 2}}$

Accepted Answer

A)  $\frac{1}{x^{22 / 7}}$ 
B)  $\frac{1}{\mathrm{x}^{11 / 5}}$ 
C)  $x^{22 / 7}$ 
D)  $x^{11 / 5}$ 
A)  $\frac{1}{x^{22 / 7}}$ 
B)  $\frac{1}{\mathrm{x}^{11 / 5}}$ 
C)  $x^{22 / 7}$ 
D)  $x^{11 / 5}$

Question 7

The negative square root of 25 is 5.

Accepted Answer

A) True 
 B)False

Question 8

Express the radical in simplified form.Assume that all variables represent positive real numbers.
-$\sqrt[4]{81 a^{4}}$

Accepted Answer

A)  $3 a^{2}$ 
B)  $81 \mathrm{a}$ 
C)  $3 a$ 
D)  $3 \sqrt{\mathrm{a}}$ 
A)  $3 a^{2}$ 
B)  $81 \mathrm{a}$ 
C)  $3 a$ 
D)  $3 \sqrt{\mathrm{a}}$

Question 9

Add or subtract as indicated. Write your answer in the form $a+b i$.
-$[(2+6 \mathrm{i})-(10+10 \mathrm{i})]-(3-7 \mathrm{i})$

Accepted Answer

A)  $15+9 i$ 
B)  $15+3 \mathrm{i}$ 
C)  $-11+3 \mathrm{i}$ 
D)  $-11+9 i$ 
A)  $15+9 i$ 
B)  $15+3 \mathrm{i}$ 
C)  $-11+3 \mathrm{i}$ 
D)  $-11+9 i$

Question 10

Choose the one alternative that best completes the statement or answers the question.
Solve the equation
-$\sqrt{3 x+10}=5-2 x$

Accepted Answer

A)  $\left\{\frac{3}{4}\right\}$ 
B)  $\left\{\frac{3}{4}, 5\right\}$ 
C)  $\left\{\frac{5}{4}, 9\right\}$ 
D)  $\{5\}$ 
A)  $\left\{\frac{3}{4}\right\}$ 
B)  $\left\{\frac{3}{4}, 5\right\}$ 
C)  $\left\{\frac{5}{4}, 9\right\}$ 
D)  $\{5\}$

Question 11

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.
-$\sqrt[4]{\frac{625}{81}}$

Accepted Answer

A)  $\frac{625}{81}$ 
B)  $\frac{5}{3}$ 
C)  $\frac{125}{27}$ 
D)  $\frac{25}{9}$ 
A)  $\frac{625}{81}$ 
B)  $\frac{5}{3}$ 
C)  $\frac{125}{27}$ 
D)  $\frac{25}{9}$

Question 12

Choose the one alternative that best completes the statement or answers the question.
Simplify. Assume that all variables represent positive real numbers.
-$5 \sqrt{32 x^{2}}-2 \sqrt{18 x^{2}}-\sqrt{2 x^{2}}$

Accepted Answer

A)  $2 x \sqrt{14}$ 
B)  $14 x \sqrt{2}$ 
C)  $13 x \sqrt{2}$ 
D)  $3 x \sqrt{14}$ 
A)  $2 x \sqrt{14}$ 
B)  $14 x \sqrt{2}$ 
C)  $13 x \sqrt{2}$ 
D)  $3 x \sqrt{14}$

Question 13

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.
-$\sqrt{64}$

Accepted Answer

A)  4096 
B)  8 
C)  $\frac{1}{64}$ 
D)  Not a real number 
A)  4096 
B)  8 
C)  $\frac{1}{64}$ 
D)  Not a real number

Question 14

Add or subtract as indicated. Write your answer in the form $a+b i$.
-$5 \mathrm{i}+(-9-\mathrm{i})$

Accepted Answer

A)  $9-6 \mathrm{i}$ 
B)  $-9+4 i$ 
C)  $-9+6 i$ 
D)  $9-4 \mathrm{i}$ 
A)  $9-6 \mathrm{i}$ 
B)  $-9+4 i$ 
C)  $-9+6 i$ 
D)  $9-4 \mathrm{i}$

Question 15

Express the radical in simplified form.Assume that all variables represent positive real numbers.
-$\sqrt[5]{128}$

Accepted Answer

A)  $2 \sqrt[5]{4}$ 
B)  $4 \sqrt{2}$ 
C)  $2+\sqrt[5]{4}$ 
D)  Not a real number 
A)  $2 \sqrt[5]{4}$ 
B)  $4 \sqrt{2}$ 
C)  $2+\sqrt[5]{4}$ 
D)  Not a real number

Question 16

Choose the one alternative that best completes the statement or answers the question.
Evaluate
-$641 / 3$

Accepted Answer

A)  256 
B)  4 
C)  12 
D)  768 
A)  256 
B)  4 
C)  12 
D)  768

Question 17

$(9-9 i)(2+9 i)$

Accepted Answer

A)  $99+63 i$ 
B)  $-81 i^{2}+63 i+18$ 
C)  $99-63 \mathrm{i}$ 
D)  $-63-99 i$ 
A)  $99+63 i$ 
B)  $-81 i^{2}+63 i+18$ 
C)  $99-63 \mathrm{i}$ 
D)  $-63-99 i$

Question 18

Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero.
-$\frac{5 x}{\sqrt{9+x}}$

Accepted Answer

A)  $\frac{5 x}{9+x}$ 
B)  $5 x \sqrt{9+x}$ 
C)  $\frac{5 x \sqrt{9+x}}{9+x}$ 
D)  $5 x$ 
A)  $\frac{5 x}{9+x}$ 
B)  $5 x \sqrt{9+x}$ 
C)  $\frac{5 x \sqrt{9+x}}{9+x}$ 
D)  $5 x$

Question 19

Simplify the radical. Assume that all variables represent positive real numbers
-$\sqrt{\frac{25}{49}}$

Accepted Answer

A)  35 
B)  1 
C)  $\frac{5}{7}$ 
D)  $\frac{7}{5}$ 
A)  35 
B)  1 
C)  $\frac{5}{7}$ 
D)  $\frac{7}{5}$

Question 20

A manufacturer's cost is given by $C=500 n^{1 / 3}+1800$, where $C$ is the cost in dollars and $n$ is the number of parts produced. Find the cost when 512 parts are produced.

Accepted Answer

A)  $\$ 63$ 
B)  $\$ 13,115$ 
C)  $\$ 5800$ 
D)  $\$ 3800$ 
A)  $\$ 63$ 
B)  $\$ 13,115$ 
C)  $\$ 5800$ 
D)  $\$ 3800$

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - $\sqrt{u^{32}}$

Write the expression in the form a + bi. - $\frac{-7+11 \mathrm{i}}{-20 \mathrm{i}}$

Simplify the expression involving rational exponents. - $\left(-\frac{64}{125}\right)^{-4 / 3}$

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt[3]{-64}$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{9 a-2}-\sqrt{6 a+6}=0$

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $\frac{x^{1 / 2} \cdot x^{3 / 10} \cdot x^{2 / 5}}{\left(x^{2}\right)^{-1 / 2}}$

The negative square root of 25 is 5.

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt[4]{81 a^{4}}$

Add or subtract as indicated. Write your answer in the form $a+b i$ . - $[(2+6 \mathrm{i})-(10+10 \mathrm{i})]-(3-7 \mathrm{i})$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{3 x+10}=5-2 x$

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $\sqrt[4]{\frac{625}{81}}$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $5 \sqrt{32 x^{2}}-2 \sqrt{18 x^{2}}-\sqrt{2 x^{2}}$

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $\sqrt{64}$

Add or subtract as indicated. Write your answer in the form $a+b i$ . - $5 \mathrm{i}+(-9-\mathrm{i})$

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt[5]{128}$

Choose the one alternative that best completes the statement or answers the question. Evaluate - $641 / 3$

$(9-9 i)(2+9 i)$

Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero. - $\frac{5 x}{\sqrt{9+x}}$

Simplify the radical. Assume that all variables represent positive real numbers - $\sqrt{\frac{25}{49}}$

A manufacturer's cost is given by $C=500 n^{1 / 3}+1800$ , where $C$ is the cost in dollars and $n$ is the number of parts produced. Find the cost when 512 parts are produced.

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 8: Roots, Radicals, and Root Functions

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - u32\sqrt{u^{32}}u32​

Write the expression in the form a + bi. - −7+11i−20i\frac{-7+11 \mathrm{i}}{-20 \mathrm{i}}−20i−7+11i​

Simplify the expression involving rational exponents. - (−64125)−4/3\left(-\frac{64}{125}\right)^{-4 / 3}(−12564​)−4/3

Express the radical in simplified form.Assume that all variables represent positive real numbers. - −643\sqrt[3]{-64}3−64​

Choose the one alternative that best completes the statement or answers the question. Solve the equation - 9a−2−6a+6=0\sqrt{9 a-2}-\sqrt{6 a+6}=09a−2​−6a+6​=0

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - x1/2⋅x3/10⋅x2/5(x2)−1/2\frac{x^{1 / 2} \cdot x^{3 / 10} \cdot x^{2 / 5}}{\left(x^{2}\right)^{-1 / 2}}(x2)−1/2x1/2⋅x3/10⋅x2/5​

The negative square root of 25 is 5.

Express the radical in simplified form.Assume that all variables represent positive real numbers. - 81a44\sqrt[4]{81 a^{4}}481a4​

Add or subtract as indicated. Write your answer in the form a+bia+b ia+bi . - [(2+6i)−(10+10i)]−(3−7i)[(2+6 \mathrm{i})-(10+10 \mathrm{i})]-(3-7 \mathrm{i})[(2+6i)−(10+10i)]−(3−7i)

Choose the one alternative that best completes the statement or answers the question. Solve the equation - 3x+10=5−2x\sqrt{3 x+10}=5-2 x3x+10​=5−2x

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - 625814\sqrt[4]{\frac{625}{81}}481625​​

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - 532x2−218x2−2x25 \sqrt{32 x^{2}}-2 \sqrt{18 x^{2}}-\sqrt{2 x^{2}}532x2​−218x2​−2x2​

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - 64\sqrt{64}64​

Add or subtract as indicated. Write your answer in the form a+bia+b ia+bi . - 5i+(−9−i)5 \mathrm{i}+(-9-\mathrm{i})5i+(−9−i)

Express the radical in simplified form.Assume that all variables represent positive real numbers. - 1285\sqrt[5]{128}5128​

Choose the one alternative that best completes the statement or answers the question. Evaluate - 641/3641 / 3641/3

(9−9i)(2+9i)(9-9 i)(2+9 i)(9−9i)(2+9i)

Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero. - 5x9+x\frac{5 x}{\sqrt{9+x}}9+x​5x​

Simplify the radical. Assume that all variables represent positive real numbers - 2549\sqrt{\frac{25}{49}}4925​​

A manufacturer's cost is given by C=500n1/3+1800C=500 n^{1 / 3}+1800C=500n1/3+1800 , where CCC is the cost in dollars and nnn is the number of parts produced. Find the cost when 512 parts are produced.

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - $\sqrt{u^{32}}$

Write the expression in the form a + bi. - $\frac{-7+11 \mathrm{i}}{-20 \mathrm{i}}$

Simplify the expression involving rational exponents. - $\left(-\frac{64}{125}\right)^{-4 / 3}$

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt[3]{-64}$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{9 a-2}-\sqrt{6 a+6}=0$

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $\frac{x^{1 / 2} \cdot x^{3 / 10} \cdot x^{2 / 5}}{\left(x^{2}\right)^{-1 / 2}}$

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt[4]{81 a^{4}}$

Add or subtract as indicated. Write your answer in the form $a+b i$ . - $[(2+6 \mathrm{i})-(10+10 \mathrm{i})]-(3-7 \mathrm{i})$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{3 x+10}=5-2 x$

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $\sqrt[4]{\frac{625}{81}}$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $5 \sqrt{32 x^{2}}-2 \sqrt{18 x^{2}}-\sqrt{2 x^{2}}$

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $\sqrt{64}$

Add or subtract as indicated. Write your answer in the form $a+b i$ . - $5 \mathrm{i}+(-9-\mathrm{i})$

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt[5]{128}$

Choose the one alternative that best completes the statement or answers the question. Evaluate - $641 / 3$

$(9-9 i)(2+9 i)$

Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero. - $\frac{5 x}{\sqrt{9+x}}$

Simplify the radical. Assume that all variables represent positive real numbers - $\sqrt{\frac{25}{49}}$

A manufacturer's cost is given by $C=500 n^{1 / 3}+1800$ , where $C$ is the cost in dollars and $n$ is the number of parts produced. Find the cost when 512 parts are produced.