Question 1

Write the expression in the form a + bi.
-$\frac{3-\mathrm{i}}{-5+8 \mathrm{i}}$

Accepted Answer

A)  $\frac{1}{89}-\frac{19}{89} \mathrm{i}$ 
B)  $-\frac{19}{89} \mathrm{i}$ 
C)  $\frac{23}{89}-\frac{19}{89} \mathrm{i}$ 
D)  $-\frac{23}{89}-\frac{19}{89} \mathrm{i}$ 
A)  $\frac{1}{89}-\frac{19}{89} \mathrm{i}$ 
B)  $-\frac{19}{89} \mathrm{i}$ 
C)  $\frac{23}{89}-\frac{19}{89} \mathrm{i}$ 
D)  $-\frac{23}{89}-\frac{19}{89} \mathrm{i}$

Question 2

The cost of manufacturing clocks is given by $c=49 \sqrt{n+9}$, where $c$ is the total cost and $n$ is the number produced. What is the cost when no clocks are produced?

Accepted Answer

A)  441 
B)  49 
C)  147 
D)  21 
A)  441 
B)  49 
C)  147 
D)  21

Question 3

The cost of manufacturing clocks is given by $c=9(n+49)^{1 / 2}$, where $c$ is the cost in dollars and $n$ is the number produced. What is the cost when no clocks are produced?

Accepted Answer

A)  $\$ 9$ 
B)  $\$ 21$ 
C)  $\$ 63$ 
D)  $\$ 441$ 
A)  $\$ 9$ 
B)  $\$ 21$ 
C)  $\$ 63$ 
D)  $\$ 441$

Question 4

Simplify. Assume that all variables represent positive real numbers.
-$\sqrt[3]{\frac{4}{7}}$

Accepted Answer

A)  $\frac{\sqrt[3]{196}}{7}$ 
B)  $\frac{\sqrt[3]{1372}}{7}$ 
C)  $\frac{196}{7}$ 
D)  $\frac{\sqrt[3]{28}}{7}$ 
A)  $\frac{\sqrt[3]{196}}{7}$ 
B)  $\frac{\sqrt[3]{1372}}{7}$ 
C)  $\frac{196}{7}$ 
D)  $\frac{\sqrt[3]{28}}{7}$

Question 5

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.
-$\left(\frac{x^{4}}{y^{-8}}\right)^{1 / 4}$

Accepted Answer

A)  $x y$ 
B)  $x y^{1 / 2}$ 
C)  $\frac{x}{y^{2}}$ 
D)  $x y^{2}$ 
A)  $x y$ 
B)  $x y^{1 / 2}$ 
C)  $\frac{x}{y^{2}}$ 
D)  $x y^{2}$

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.
-$\left(\mathrm{r}^{1 / 6_{\mathrm{s}}} 1 / 6\right)^{2}$

Accepted Answer

A)  $r^{1 / 3} s^{1 / 3}$ 
B)  $\mathrm{r}^{1 / 36_{\mathrm{s}} 1 / 36}$ 
C)  $\mathrm{r}^{2} \mathrm{~s}^{2}$ 
D)  $\mathrm{r}^{1 / 12} \mathrm{~s}^{1 / 12}$ 
A)  $r^{1 / 3} s^{1 / 3}$ 
B)  $\mathrm{r}^{1 / 36_{\mathrm{s}} 1 / 36}$ 
C)  $\mathrm{r}^{2} \mathrm{~s}^{2}$ 
D)  $\mathrm{r}^{1 / 12} \mathrm{~s}^{1 / 12}$

Question 7

Simplify the expression involving rational exponents.
-$216^{4 / 3}$

Accepted Answer

A)  1296 
B)  7776 
C)  279,936 
D)  46,656 
A)  1296 
B)  7776 
C)  279,936 
D)  46,656

Question 8

The principal square root of 9 is 3.

Accepted Answer

A) True 
 B)False

Question 9

Multiply or divide as indicated.
-$\sqrt{-2} \cdot \sqrt{-2}$

Accepted Answer

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

Question 10

Multiply, then simplify the product. Assume that all variables represent positive real numbers.
-$(\sqrt{3}+5)(\sqrt{2}-3)$

Accepted Answer

A)  $\sqrt{6}+2 \sqrt{2}-15$ 
B)  $3 \sqrt{6}-15$ 
C)  $\sqrt{6}-15$ 
D)  $\sqrt{6}-3 \sqrt{3}+5 \sqrt{2}-15$ 
A)  $\sqrt{6}+2 \sqrt{2}-15$ 
B)  $3 \sqrt{6}-15$ 
C)  $\sqrt{6}-15$ 
D)  $\sqrt{6}-3 \sqrt{3}+5 \sqrt{2}-15$

Question 11

The length of the diagonal of a rectangle is given by $D=\sqrt{L^{2}+W^{2}}$ where $L$ and $W$ are the length and width of the rectangle. What is the length of the diagonal, $\mathrm{D}$, of a rectangle that is 98 inches long and 49 inches wide? Round your answer to the nearest tenth of an inch, if necessary.

Accepted Answer

A)  69.3 in. 
B)  109.6 in. 
C)  84.9 in. 
D)  $12.1 \mathrm{in}$. 
A)  69.3 in. 
B)  109.6 in. 
C)  84.9 in. 
D)  $12.1 \mathrm{in}$.

Question 12

Choose the one alternative that best completes the statement or answers the question.
Solve the equation
-$\sqrt[4]{\mathrm{x}+5}+5=0$

Accepted Answer

A)  $\{125\}$ 
B)  $\{-125\}$ 
C)  $\{1\}$ 
D)  $\varnothing$ 
A)  $\{125\}$ 
B)  $\{-125\}$ 
C)  $\{1\}$ 
D)  $\varnothing$

Question 13

Rationalize the denominator. Assume that all variables represent positive real numbers. 
-$\frac{4}{\sqrt{19}}$

Accepted Answer

A)  365 
B)  $4 \sqrt{19}$ 
C)  $\frac{16 \sqrt{19}}{19}$ 
D)  $\frac{4 \sqrt{19}}{19}$ 
A)  365 
B)  $4 \sqrt{19}$ 
C)  $\frac{16 \sqrt{19}}{19}$ 
D)  $\frac{4 \sqrt{19}}{19}$

Question 14

Provide an appropriate response.
-If $a>0$, then $\frac{a}{i}=i a$.

Accepted Answer

A) True 
 B)False

Question 15

Simplify. Assume that all variables represent positive real numbers.
-$\frac{-50}{\sqrt{13}+\sqrt{3}}$

Accepted Answer

A)  $-(\sqrt{13}-\sqrt{3})$ 
B)  $-5(\sqrt{13}-\sqrt{3})$ 
C)  $5(\sqrt{13}-\sqrt{3})$ 
D)  $-5(\sqrt{13}+\sqrt{3})$ 
A)  $-(\sqrt{13}-\sqrt{3})$ 
B)  $-5(\sqrt{13}-\sqrt{3})$ 
C)  $5(\sqrt{13}-\sqrt{3})$ 
D)  $-5(\sqrt{13}+\sqrt{3})$

Question 16

Simplify the expression involving rational exponents.
-$256^{1 / 4}$

Accepted Answer

A)  4 
B)  64 
C)  1024 
D)  16 
A)  4 
B)  64 
C)  1024 
D)  16

Question 17

Rationalize the numerator. Assume that all variables represent positive real numbers.
-$\frac{4-\sqrt{3}}{6}$

Accepted Answer

A)  $\frac{19}{24+4 \sqrt{3}}$ 
B)  $\frac{13}{24+6 \sqrt{3}}$ 
C)  $\frac{5}{24+4 \sqrt{3}}$ 
D)  $\frac{5}{24+6 \sqrt{3}}$ 
A)  $\frac{19}{24+4 \sqrt{3}}$ 
B)  $\frac{13}{24+6 \sqrt{3}}$ 
C)  $\frac{5}{24+4 \sqrt{3}}$ 
D)  $\frac{5}{24+6 \sqrt{3}}$

Question 18

Simplify the expression. Assume that all variables represent positive real numbers.
-$(-216)^{-2 / 3}$

Accepted Answer

A)  $-\frac{1}{36}$ 
B)  36 
C)  $\frac{1}{36}$ 
D)  -36 
A)  $-\frac{1}{36}$ 
B)  36 
C)  $\frac{1}{36}$ 
D)  -36

Question 19

Can the sum be simplified without first simplifying the individual radical expressions? $7 \sqrt[12]{10}+9 \sqrt[12]{10}$

Accepted Answer

A) True 
 B)False

Question 20

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.
-$\sqrt[3]{\mathrm{r}} \cdot \sqrt[7]{\mathrm{r}^{3}}$

Accepted Answer

A)  $\sqrt[21]{\mathrm{r}^{4}}$ 
B)  $\sqrt[21]{\mathrm{r}^{16}}$ 
C)  $\sqrt[10]{\mathrm{r}^{3}}$ 
D)  $\sqrt[10]{r^{4}}$ 
A)  $\sqrt[21]{\mathrm{r}^{4}}$ 
B)  $\sqrt[21]{\mathrm{r}^{16}}$ 
C)  $\sqrt[10]{\mathrm{r}^{3}}$ 
D)  $\sqrt[10]{r^{4}}$

Write the expression in the form a + bi. - $\frac{3-\mathrm{i}}{-5+8 \mathrm{i}}$

The cost of manufacturing clocks is given by $c=49 \sqrt{n+9}$ , where $c$ is the total cost and $n$ is the number produced. What is the cost when no clocks are produced?

The cost of manufacturing clocks is given by $c=9(n+49)^{1 / 2}$ , where $c$ is the cost in dollars and $n$ is the number produced. What is the cost when no clocks are produced?

Simplify. Assume that all variables represent positive real numbers. - $\sqrt[3]{\frac{4}{7}}$

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $\left(\frac{x^{4}}{y^{-8}}\right)^{1 / 4}$

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $\left(\mathrm{r}^{1 / 6_{\mathrm{s}}} 1 / 6\right)^{2}$

Simplify the expression involving rational exponents. - $216^{4 / 3}$

The principal square root of 9 is 3.

Multiply or divide as indicated. - $\sqrt{-2} \cdot \sqrt{-2}$

Multiply, then simplify the product. Assume that all variables represent positive real numbers. - $(\sqrt{3}+5)(\sqrt{2}-3)$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt[4]{\mathrm{x}+5}+5=0$

Rationalize the denominator. Assume that all variables represent positive real numbers. - $\frac{4}{\sqrt{19}}$

Provide an appropriate response. -If $a>0$ , then $\frac{a}{i}=i a$ .

Simplify. Assume that all variables represent positive real numbers. - $\frac{-50}{\sqrt{13}+\sqrt{3}}$

Simplify the expression involving rational exponents. - $256^{1 / 4}$

Rationalize the numerator. Assume that all variables represent positive real numbers. - $\frac{4-\sqrt{3}}{6}$

Simplify the expression. Assume that all variables represent positive real numbers. - $(-216)^{-2 / 3}$

Can the sum be simplified without first simplifying the individual radical expressions? $7 \sqrt[12]{10}+9 \sqrt[12]{10}$

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - $\sqrt[3]{\mathrm{r}} \cdot \sqrt[7]{\mathrm{r}^{3}}$

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

Write the expression in the form a + bi. - 3−i−5+8i\frac{3-\mathrm{i}}{-5+8 \mathrm{i}}−5+8i3−i​

The cost of manufacturing clocks is given by c=49n+9c=49 \sqrt{n+9}c=49n+9​ , where ccc is the total cost and nnn is the number produced. What is the cost when no clocks are produced?

The cost of manufacturing clocks is given by c=9(n+49)1/2c=9(n+49)^{1 / 2}c=9(n+49)1/2 , where ccc is the cost in dollars and nnn is the number produced. What is the cost when no clocks are produced?

Simplify. Assume that all variables represent positive real numbers. - 473\sqrt[3]{\frac{4}{7}}374​​

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - (x4y−8)1/4\left(\frac{x^{4}}{y^{-8}}\right)^{1 / 4}(y−8x4​)1/4

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - (r1/6s1/6)2\left(\mathrm{r}^{1 / 6_{\mathrm{s}}} 1 / 6\right)^{2}(r1/6s​1/6)2

Simplify the expression involving rational exponents. - 2164/3216^{4 / 3}2164/3

The principal square root of 9 is 3.

Multiply or divide as indicated. - −2⋅−2\sqrt{-2} \cdot \sqrt{-2}−2​⋅−2​

Multiply, then simplify the product. Assume that all variables represent positive real numbers. - (3+5)(2−3)(\sqrt{3}+5)(\sqrt{2}-3)(3​+5)(2​−3)

Choose the one alternative that best completes the statement or answers the question. Solve the equation - x+54+5=0\sqrt[4]{\mathrm{x}+5}+5=04x+5​+5=0

Rationalize the denominator. Assume that all variables represent positive real numbers. - 419\frac{4}{\sqrt{19}}19​4​

Provide an appropriate response. -If a>0a>0a>0 , then ai=ia\frac{a}{i}=i aia​=ia .

Simplify. Assume that all variables represent positive real numbers. - −5013+3\frac{-50}{\sqrt{13}+\sqrt{3}}13​+3​−50​

Simplify the expression involving rational exponents. - 2561/4256^{1 / 4}2561/4

Rationalize the numerator. Assume that all variables represent positive real numbers. - 4−36\frac{4-\sqrt{3}}{6}64−3​​

Simplify the expression. Assume that all variables represent positive real numbers. - (−216)−2/3(-216)^{-2 / 3}(−216)−2/3

Can the sum be simplified without first simplifying the individual radical expressions? 71012+910127 \sqrt[12]{10}+9 \sqrt[12]{10}71210​+91210​

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - r3⋅r37\sqrt[3]{\mathrm{r}} \cdot \sqrt[7]{\mathrm{r}^{3}}3r​⋅7r3​

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

Write the expression in the form a + bi. - $\frac{3-\mathrm{i}}{-5+8 \mathrm{i}}$

The cost of manufacturing clocks is given by $c=49 \sqrt{n+9}$ , where $c$ is the total cost and $n$ is the number produced. What is the cost when no clocks are produced?

The cost of manufacturing clocks is given by $c=9(n+49)^{1 / 2}$ , where $c$ is the cost in dollars and $n$ is the number produced. What is the cost when no clocks are produced?

Simplify. Assume that all variables represent positive real numbers. - $\sqrt[3]{\frac{4}{7}}$

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $\left(\frac{x^{4}}{y^{-8}}\right)^{1 / 4}$

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $\left(\mathrm{r}^{1 / 6_{\mathrm{s}}} 1 / 6\right)^{2}$

Simplify the expression involving rational exponents. - $216^{4 / 3}$

Multiply or divide as indicated. - $\sqrt{-2} \cdot \sqrt{-2}$

Multiply, then simplify the product. Assume that all variables represent positive real numbers. - $(\sqrt{3}+5)(\sqrt{2}-3)$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt[4]{\mathrm{x}+5}+5=0$

Rationalize the denominator. Assume that all variables represent positive real numbers. - $\frac{4}{\sqrt{19}}$

Provide an appropriate response. -If $a>0$ , then $\frac{a}{i}=i a$ .

Simplify. Assume that all variables represent positive real numbers. - $\frac{-50}{\sqrt{13}+\sqrt{3}}$

Simplify the expression involving rational exponents. - $256^{1 / 4}$

Rationalize the numerator. Assume that all variables represent positive real numbers. - $\frac{4-\sqrt{3}}{6}$

Simplify the expression. Assume that all variables represent positive real numbers. - $(-216)^{-2 / 3}$

Can the sum be simplified without first simplifying the individual radical expressions? $7 \sqrt[12]{10}+9 \sqrt[12]{10}$

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - $\sqrt[3]{\mathrm{r}} \cdot \sqrt[7]{\mathrm{r}^{3}}$