Question 1

$(3-8 \mathrm{i})(5-2 \mathrm{i})$

Accepted Answer

A)  $-1-46 \mathrm{i}$ 
B)  $-1+46 i$ 
C)  $16 i^{2}-46 i+15$ 
D)  $31-34 \mathrm{i}$ 
A)  $-1-46 \mathrm{i}$ 
B)  $-1+46 i$ 
C)  $16 i^{2}-46 i+15$ 
D)  $31-34 \mathrm{i}$

Question 2

Choose the one alternative that best completes the statement or answers the question.
Solve the equation
-$\sqrt{4 q+5}=5$

Accepted Answer

A)  $\{25\}$ 
B)  $\left\{\frac{25}{4}\right\}$ 
C)  $\left\{\frac{15}{2}\right\}$ 
D)  $\{5\}$ 
A)  $\{25\}$ 
B)  $\left\{\frac{25}{4}\right\}$ 
C)  $\left\{\frac{15}{2}\right\}$ 
D)  $\{5\}$

Question 3

Write with radicals. Assume that all variables represent positive real numbers
-$(4 m+n)^{4 / 5}$

Accepted Answer

A)  $\sqrt[4]{4 m+n^{5}}$ 
B)  $\sqrt[5]{4 m+n^{4}}$ 
C)  $\sqrt[5]{(4 m+n)^{4}}$ 
D)  $\sqrt[4]{(4 m+n)^{5}}$ 
A)  $\sqrt[4]{4 m+n^{5}}$ 
B)  $\sqrt[5]{4 m+n^{4}}$ 
C)  $\sqrt[5]{(4 m+n)^{4}}$ 
D)  $\sqrt[4]{(4 m+n)^{5}}$

Question 4

Perform the indicated operation. Give answer in standard form.
-$\mathrm{i}^{5}$

Accepted Answer

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

Question 5

Choose the one alternative that best completes the statement or answers the question.
Solve the equation
-$4 \sqrt{\mathrm{x}}=\sqrt{9 \mathrm{x}+9}$

Accepted Answer

A)  $\left\{-\frac{9}{5}\right\}$ 
B)  $\left\{\frac{9}{25}\right\}$ 
C)  $\left\{\frac{9}{7}\right\}$ 
D)  $\left\{-\frac{9}{8}\right\}$ 
A)  $\left\{-\frac{9}{5}\right\}$ 
B)  $\left\{\frac{9}{25}\right\}$ 
C)  $\left\{\frac{9}{7}\right\}$ 
D)  $\left\{-\frac{9}{8}\right\}$

Question 6

Choose the one alternative that best completes the statement or answers the question.
Simplify. Assume that all variables represent positive real numbers.
-$3 \sqrt[3]{\mathrm{a}}+\sqrt[3]{8 \mathrm{a}}$

Accepted Answer

A)  $4 \sqrt[3]{8 a}$ 
B)  $5 \sqrt[3]{a}$ 
C)  $6 \sqrt[3]{a}$ 
D)  $3 \sqrt[3]{a}+\sqrt[3]{8 a}$ 
A)  $4 \sqrt[3]{8 a}$ 
B)  $5 \sqrt[3]{a}$ 
C)  $6 \sqrt[3]{a}$ 
D)  $3 \sqrt[3]{a}+\sqrt[3]{8 a}$

Question 7

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.
-$6 x^{6 / 5}\left(x^{11 / 5}-2 x\right)$

Accepted Answer

A)  $\frac{6}{x^{17 / 5}}-12 x^{11 / 5}$ 
B)  $\frac{6}{x^{17 / 5}}-\frac{12}{x^{11 / 5}}$ 
C)  $6 x^{17 / 5}-\frac{12}{x^{11 / 5}}$ 
D)  $6 x^{17 / 5}-12 x^{11 / 5}$ 
A)  $\frac{6}{x^{17 / 5}}-12 x^{11 / 5}$ 
B)  $\frac{6}{x^{17 / 5}}-\frac{12}{x^{11 / 5}}$ 
C)  $6 x^{17 / 5}-\frac{12}{x^{11 / 5}}$ 
D)  $6 x^{17 / 5}-12 x^{11 / 5}$

Question 8

Graph the circle.
-$(x-2)^{2}+(y-4)^{2}=25$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 9

Choose the one alternative that best completes the statement or answers the question.
-A rectangle has a length of $\sqrt{221}$ and a width of $\sqrt{171}$. What is the best estimate for its dimensions?

Accepted Answer

A)  14 by 13 
B)  15 by 13 
C)  14 by 14 
D)  15 by 14 
A)  14 by 13 
B)  15 by 13 
C)  14 by 14 
D)  15 by 14

Question 10

$\left(7 m^{4}+3 k^{2}\right)^{-4 / 3}$

Accepted Answer

A)  $\frac{1}{\left(\sqrt[3]{7 m^{4}+3 k^{2}}\right)^{4}}$ 
B)  $\left(\sqrt[3]{7 m^{4}+3 k^{2}}\right)^{4}$ 
C)  $\frac{1}{\left(\sqrt[4]{7 m^{4}+3 k^{2}}\right)^{3}}$ 
D)  $\left(\sqrt[4]{7 m^{4}+3 k^{2}}\right)^{3}$ 
A)  $\frac{1}{\left(\sqrt[3]{7 m^{4}+3 k^{2}}\right)^{4}}$ 
B)  $\left(\sqrt[3]{7 m^{4}+3 k^{2}}\right)^{4}$ 
C)  $\frac{1}{\left(\sqrt[4]{7 m^{4}+3 k^{2}}\right)^{3}}$ 
D)  $\left(\sqrt[4]{7 m^{4}+3 k^{2}}\right)^{3}$

Question 11

In an economics study, three quantities $m, p$, and $q$ have been found to be related by the equation $\mathrm{m}=\mathrm{p}^{1 / 2} \cdot \mathrm{q}^{1 / 2}$. Find $\mathrm{m}$, if $\mathrm{p}=16$ and $\mathrm{q}=25$.

Accepted Answer

A)  9 
B)  20 
C)  400 
D)  100 
A)  9 
B)  20 
C)  400 
D)  100

Question 12

The easiest way to simplify the expression $\frac{9}{8-\sqrt{8}}$ is to multiply both the numerator and denominator by $8+\sqrt{8}$.

Accepted Answer

A) True 
 B)False

Question 13

Simplify. Assume that all variables represent positive real numbers.
-$\sqrt{192}-3 \sqrt{48}-3 \sqrt{108}$

Accepted Answer

A)  $36 \sqrt{3}$ 
B)  $-22 \sqrt{3}$ 
C)  $-48 \sqrt{3}$ 
D)  $22 \sqrt{3}$ 
A)  $36 \sqrt{3}$ 
B)  $-22 \sqrt{3}$ 
C)  $-48 \sqrt{3}$ 
D)  $22 \sqrt{3}$

Question 14

Write with rational exponents and then apply the properties of exponents. Assume that all radicands represent positive real numbers. Give answers in exponential form.
-$\frac{\sqrt{x^{5}}}{\sqrt{x^{14}}}$

Accepted Answer

A)  $x^{9 / 2}$ 
B)  $\frac{1}{x^{19 / 2}}$ 
C)  $\frac{1}{\mathrm{x}^{18}}$ 
D)  $\frac{1}{x^{9 / 2}}$ 
A)  $x^{9 / 2}$ 
B)  $\frac{1}{x^{19 / 2}}$ 
C)  $\frac{1}{\mathrm{x}^{18}}$ 
D)  $\frac{1}{x^{9 / 2}}$

Question 15

Can the sum be simplified without first simplifying the individual radical expressions? $6 \sqrt[12]{40,000}+2 \sqrt[12]{64}$

Accepted Answer

A) True 
 B)False

Question 16

Choose the one alternative that best completes the statement or answers the question.
Simplify. Assume that all variables represent positive real numbers.
-$3 \sqrt[3]{8 x}+3 \sqrt[3]{64 x}$

Accepted Answer

A)  $18 x$ 
B)  $3 \sqrt[3]{72 x}$ 
C)  $6 \sqrt[3]{x}$ 
D)  $18 \sqrt[3]{x}$ 
A)  $18 x$ 
B)  $3 \sqrt[3]{72 x}$ 
C)  $6 \sqrt[3]{x}$ 
D)  $18 \sqrt[3]{x}$

Question 17

Explain the procedure you would use to find the quotient $\frac{-5+4 \mathrm{i}}{-3+5 \mathrm{i}}$. Do not actually find the quotient.

Accepted Answer

Multiply both the numerator and denomina

Question 18

Rewrite the expressions with rational exponents as radical expressions, and then solve the equation.
-$(2 x+5)^{1 / 2}-(x-2)^{1 / 2}=3$

Accepted Answer

A)  $\{2\}$ 
B)  $\{2,38\}$ 
C)  $\{-2\}$ 
D)  $\{3,8\}$ 
A)  $\{2\}$ 
B)  $\{2,38\}$ 
C)  $\{-2\}$ 
D)  $\{3,8\}$

Question 19

Is $\sqrt{(-2)(-8)}=4$ ?

Accepted Answer

A) True 
 B)False

Question 20

The easiest way to simplify the expression $3 \sqrt{\frac{4}{7}}$ is to multiply both the numerator and denominator of $\frac{\sqrt[3]{4}}{\sqrt[3]{7}}$ by $\sqrt[3]{7}$.

Accepted Answer

A) True 
 B)False

$(3-8 \mathrm{i})(5-2 \mathrm{i})$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{4 q+5}=5$

Write with radicals. Assume that all variables represent positive real numbers - $(4 m+n)^{4 / 5}$

Perform the indicated operation. Give answer in standard form. - $\mathrm{i}^{5}$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $4 \sqrt{\mathrm{x}}=\sqrt{9 \mathrm{x}+9}$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $3 \sqrt[3]{\mathrm{a}}+\sqrt[3]{8 \mathrm{a}}$

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $6 x^{6 / 5}\left(x^{11 / 5}-2 x\right)$

Graph the circle. - $(x-2)^{2}+(y-4)^{2}=25$ $Graph the circle. - (x-2)^{2}+(y-4)^{2}=25$

Choose the one alternative that best completes the statement or answers the question. -A rectangle has a length of $\sqrt{221}$ and a width of $\sqrt{171}$ . What is the best estimate for its dimensions?

$\left(7 m^{4}+3 k^{2}\right)^{-4 / 3}$

In an economics study, three quantities $m, p$ , and $q$ have been found to be related by the equation $\mathrm{m}=\mathrm{p}^{1 / 2} \cdot \mathrm{q}^{1 / 2}$ . Find $\mathrm{m}$ , if $\mathrm{p}=16$ and $\mathrm{q}=25$ .

The easiest way to simplify the expression $\frac{9}{8-\sqrt{8}}$ is to multiply both the numerator and denominator by $8+\sqrt{8}$ .

Simplify. Assume that all variables represent positive real numbers. - $\sqrt{192}-3 \sqrt{48}-3 \sqrt{108}$

Write with rational exponents and then apply the properties of exponents. Assume that all radicands represent positive real numbers. Give answers in exponential form. - $\frac{\sqrt{x^{5}}}{\sqrt{x^{14}}}$

Can the sum be simplified without first simplifying the individual radical expressions? $6 \sqrt[12]{40,000}+2 \sqrt[12]{64}$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $3 \sqrt[3]{8 x}+3 \sqrt[3]{64 x}$

Explain the procedure you would use to find the quotient $\frac{-5+4 \mathrm{i}}{-3+5 \mathrm{i}}$ . Do not actually find the quotient.

Rewrite the expressions with rational exponents as radical expressions, and then solve the equation. - $(2 x+5)^{1 / 2}-(x-2)^{1 / 2}=3$

Is $\sqrt{(-2)(-8)}=4$ ?

The easiest way to simplify the expression $3 \sqrt{\frac{4}{7}}$ is to multiply both the numerator and denominator of $\frac{\sqrt[3]{4}}{\sqrt[3]{7}}$ by $\sqrt[3]{7}$ .

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

(3−8i)(5−2i)(3-8 \mathrm{i})(5-2 \mathrm{i})(3−8i)(5−2i)

Choose the one alternative that best completes the statement or answers the question. Solve the equation - 4q+5=5\sqrt{4 q+5}=54q+5​=5

Write with radicals. Assume that all variables represent positive real numbers - (4m+n)4/5(4 m+n)^{4 / 5}(4m+n)4/5

Perform the indicated operation. Give answer in standard form. - i5\mathrm{i}^{5}i5

Choose the one alternative that best completes the statement or answers the question. Solve the equation - 4x=9x+94 \sqrt{\mathrm{x}}=\sqrt{9 \mathrm{x}+9}4x​=9x+9​

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - 3a3+8a33 \sqrt[3]{\mathrm{a}}+\sqrt[3]{8 \mathrm{a}}33a​+38a​

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - 6x6/5(x11/5−2x)6 x^{6 / 5}\left(x^{11 / 5}-2 x\right)6x6/5(x11/5−2x)

Graph the circle. - (x−2)2+(y−4)2=25(x-2)^{2}+(y-4)^{2}=25(x−2)2+(y−4)2=25

Choose the one alternative that best completes the statement or answers the question. -A rectangle has a length of 221\sqrt{221}221​ and a width of 171\sqrt{171}171​ . What is the best estimate for its dimensions?

(7m4+3k2)−4/3\left(7 m^{4}+3 k^{2}\right)^{-4 / 3}(7m4+3k2)−4/3

In an economics study, three quantities m,pm, pm,p , and qqq have been found to be related by the equation m=p1/2⋅q1/2\mathrm{m}=\mathrm{p}^{1 / 2} \cdot \mathrm{q}^{1 / 2}m=p1/2⋅q1/2 . Find m\mathrm{m}m , if p=16\mathrm{p}=16p=16 and q=25\mathrm{q}=25q=25 .

The easiest way to simplify the expression 98−8\frac{9}{8-\sqrt{8}}8−8​9​ is to multiply both the numerator and denominator by 8+88+\sqrt{8}8+8​ .

Simplify. Assume that all variables represent positive real numbers. - 192−348−3108\sqrt{192}-3 \sqrt{48}-3 \sqrt{108}192​−348​−3108​

Write with rational exponents and then apply the properties of exponents. Assume that all radicands represent positive real numbers. Give answers in exponential form. - x5x14\frac{\sqrt{x^{5}}}{\sqrt{x^{14}}}x14​x5​​

Can the sum be simplified without first simplifying the individual radical expressions? 640,00012+264126 \sqrt[12]{40,000}+2 \sqrt[12]{64}61240,000​+21264​

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - 38x3+364x33 \sqrt[3]{8 x}+3 \sqrt[3]{64 x}338x​+3364x​

Explain the procedure you would use to find the quotient −5+4i−3+5i\frac{-5+4 \mathrm{i}}{-3+5 \mathrm{i}}−3+5i−5+4i​ . Do not actually find the quotient.

Rewrite the expressions with rational exponents as radical expressions, and then solve the equation. - (2x+5)1/2−(x−2)1/2=3(2 x+5)^{1 / 2}-(x-2)^{1 / 2}=3(2x+5)1/2−(x−2)1/2=3

Is (−2)(−8)=4\sqrt{(-2)(-8)}=4(−2)(−8)​=4 ?

The easiest way to simplify the expression 3473 \sqrt{\frac{4}{7}}374​​ is to multiply both the numerator and denominator of 4373\frac{\sqrt[3]{4}}{\sqrt[3]{7}}37​34​​ by 73\sqrt[3]{7}37​ .

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

$(3-8 \mathrm{i})(5-2 \mathrm{i})$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{4 q+5}=5$

Write with radicals. Assume that all variables represent positive real numbers - $(4 m+n)^{4 / 5}$

Perform the indicated operation. Give answer in standard form. - $\mathrm{i}^{5}$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $4 \sqrt{\mathrm{x}}=\sqrt{9 \mathrm{x}+9}$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $3 \sqrt[3]{\mathrm{a}}+\sqrt[3]{8 \mathrm{a}}$

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $6 x^{6 / 5}\left(x^{11 / 5}-2 x\right)$

Graph the circle. - $(x-2)^{2}+(y-4)^{2}=25$ $Graph the circle. - (x-2)^{2}+(y-4)^{2}=25$

Choose the one alternative that best completes the statement or answers the question. -A rectangle has a length of $\sqrt{221}$ and a width of $\sqrt{171}$ . What is the best estimate for its dimensions?

$\left(7 m^{4}+3 k^{2}\right)^{-4 / 3}$

In an economics study, three quantities $m, p$ , and $q$ have been found to be related by the equation $\mathrm{m}=\mathrm{p}^{1 / 2} \cdot \mathrm{q}^{1 / 2}$ . Find $\mathrm{m}$ , if $\mathrm{p}=16$ and $\mathrm{q}=25$ .

The easiest way to simplify the expression $\frac{9}{8-\sqrt{8}}$ is to multiply both the numerator and denominator by $8+\sqrt{8}$ .

Simplify. Assume that all variables represent positive real numbers. - $\sqrt{192}-3 \sqrt{48}-3 \sqrt{108}$

Write with rational exponents and then apply the properties of exponents. Assume that all radicands represent positive real numbers. Give answers in exponential form. - $\frac{\sqrt{x^{5}}}{\sqrt{x^{14}}}$

Can the sum be simplified without first simplifying the individual radical expressions? $6 \sqrt[12]{40,000}+2 \sqrt[12]{64}$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $3 \sqrt[3]{8 x}+3 \sqrt[3]{64 x}$

Explain the procedure you would use to find the quotient $\frac{-5+4 \mathrm{i}}{-3+5 \mathrm{i}}$ . Do not actually find the quotient.

Rewrite the expressions with rational exponents as radical expressions, and then solve the equation. - $(2 x+5)^{1 / 2}-(x-2)^{1 / 2}=3$

Is $\sqrt{(-2)(-8)}=4$ ?

The easiest way to simplify the expression $3 \sqrt{\frac{4}{7}}$ is to multiply both the numerator and denominator of $\frac{\sqrt[3]{4}}{\sqrt[3]{7}}$ by $\sqrt[3]{7}$ .