Question 1

Choose the one alternative that best completes the statement or answers the question.
Multiply using the product rule.
-$\sqrt{5} \cdot \sqrt{3}$

Accepted Answer

A)  $\sqrt[4]{15}$ 
B)  $\sqrt{8}$ 
C)  $\sqrt{15}$ 
D)  $\sqrt[4]{8}$ 
A)  $\sqrt[4]{15}$ 
B)  $\sqrt{8}$ 
C)  $\sqrt{15}$ 
D)  $\sqrt[4]{8}$

Question 2

Simplify by first writing the radicals with the same index. Then multiply.
-$\sqrt{5} \cdot \sqrt[5]{4}$

Accepted Answer

A)  $\sqrt[10]{10,000}$ 
B)  $\sqrt[10]{50,000}$ 
C)  $\sqrt[10]{20}$ 
D)  $\sqrt[7]{50,000}$ 
A)  $\sqrt[10]{10,000}$ 
B)  $\sqrt[10]{50,000}$ 
C)  $\sqrt[10]{20}$ 
D)  $\sqrt[7]{50,000}$

Question 3

$\sqrt{9} \cdot \sqrt{25}=\sqrt{9 \cdot 25}$

Accepted Answer

A) True 
 B)False

Question 4

A manufacturer's cost is given by $C=200 \sqrt[3]{n}+1100$, where $C$ is the cost and $n$ is the number of parts produced. Find the cost when 729 parts are produced.

Accepted Answer

A)  $\$ 6500$ 
B)  $\$ 2900$ 
C)  $\$ 22$ 
D)  $\$ 2000$ 
A)  $\$ 6500$ 
B)  $\$ 2900$ 
C)  $\$ 22$ 
D)  $\$ 2000$

Question 5

Express the radical in simplified form.Assume that all variables represent positive real numbers.
-$\sqrt{-864}$

Accepted Answer

A)  Not a real number 
B)  $-12 \sqrt{6}$ 
C)  $-12 \sqrt{-6}$ 
D)  $12 \sqrt{6}$ 
A)  Not a real number 
B)  $-12 \sqrt{6}$ 
C)  $-12 \sqrt{-6}$ 
D)  $12 \sqrt{6}$

Question 6

Simplify by first writing the radicals with the same index. Then multiply.
-$\sqrt[3]{6} \cdot \sqrt[4]{2}$

Accepted Answer

A)  $\sqrt[12]{12}$ 
B)  $\sqrt[12]{10,368}$ 
C)  $\sqrt[7]{10,368}$ 
D)  $\sqrt[12]{1304}$ 
A)  $\sqrt[12]{12}$ 
B)  $\sqrt[12]{10,368}$ 
C)  $\sqrt[7]{10,368}$ 
D)  $\sqrt[12]{1304}$

Question 7

If $n$ is a positive integer, does $\sqrt[n]{x^{n}}=x$ ? Explain.

Accepted Answer

No. When @#LAT-DLM& is an odd positive i

Question 8

Simplify the expression involving rational exponents.
-$1444^{1 / 2}$

Accepted Answer

A)  38 
B)  152 
C)  19 
D)  76 
A)  38 
B)  152 
C)  19 
D)  76

Question 9

The easiest way to simplify the expression $\sqrt[3]{\frac{2}{9}}$ is to multiply both the numerator and denominator of $\frac{\sqrt[3]{2}}{\sqrt[3]{9}}$ by $\sqrt[3]{9}$

Accepted Answer

A) True 
 B)False

Question 10

Choose the one alternative that best completes the statement or answers the question.
Simplify. Assume that all variables represent positive real numbers.
-$5 \sqrt{11}+8 \sqrt{11}$

Accepted Answer

A)  $13 \sqrt{22}$ 
B)  143 
C)  $13 \sqrt{11}$ 
D)  $40 \sqrt{11}$ 
A)  $13 \sqrt{22}$ 
B)  143 
C)  $13 \sqrt{11}$ 
D)  $40 \sqrt{11}$

Question 11

Graph the circle. Identify the center.
-$(x-1)^{2}+(y-2)^{2}=4$

Accepted Answer

A)  center: $(1,2)$
  
B)  center: $(1,2)$
  
C)  center: $(-1,-2)$
  
D)  center: $(-1,-2)$
  
A)  center: $(1,2)$
  
B)  center: $(1,2)$
  
C)  center: $(-1,-2)$
  
D)  center: $(-1,-2)$

Question 12

Find the equation of a circle satisfying the given conditions.
-Center: $(0,-7)$; radius: $\sqrt{7}$

Accepted Answer

A)  $x^{2}+(y-7)^{2}=7$ 
B)  $(x+7)^{2}+y^{2}=49$ 
C)  $x^{2}+(y+7)^{2}=7$ 
D)  $(x-7)^{2}+y^{2}=49$ 
A)  $x^{2}+(y-7)^{2}=7$ 
B)  $(x+7)^{2}+y^{2}=49$ 
C)  $x^{2}+(y+7)^{2}=7$ 
D)  $(x-7)^{2}+y^{2}=49$

Question 13

Write the expression in lowest terms. Assume that all variables represent positive real numbers.
-$\frac{6 z+\sqrt{24 z^{3}}}{3 z}$

Accepted Answer

A)  $2+2 \sqrt{6 z}$ 
B)  $2+2 \sqrt{2}$ 
C)  $\frac{6+2 \sqrt{6 z}}{3}$ 
D)  $\frac{6+2 \sqrt{6}}{3}$ 
A)  $2+2 \sqrt{6 z}$ 
B)  $2+2 \sqrt{2}$ 
C)  $\frac{6+2 \sqrt{6 z}}{3}$ 
D)  $\frac{6+2 \sqrt{6}}{3}$

Question 14

The length a spring is stretched from its natural length with work, W foot-pounds, is given by
$$\mathrm{L}=\sqrt{\frac{2 \mathrm{~W}}{\mathrm{k}}}$$
Where $\mathrm{k}$ is a constant for the given spring. If a certain spring has a constant of 74.8, and the spring is to be stretched 1.9 feet from its natural length, how much work will be necessary? Round your answer to the nearest tenth.

Accepted Answer

A)  51.6 foot-pounds 
B)  135 foot-pounds 
C)  270 foot-pounds 
D)  71.1 foot-pounds 
A)  51.6 foot-pounds 
B)  135 foot-pounds 
C)  270 foot-pounds 
D)  71.1 foot-pounds

Question 15

Explain why the expression cannot be simplified further.
$\sqrt[11]{\mathrm{a}}-\sqrt[10]{\mathrm{a}}$

Accepted Answer

Indexes mu

Question 16

Simplify the expression involving rational exponents.
-$216^{-1 / 3}$

Accepted Answer

A)  -6 
B)  $\frac{1}{6}$ 
C)  $\frac{1}{7}$ 
D)  $-\frac{1}{6}$ 
A)  -6 
B)  $\frac{1}{6}$ 
C)  $\frac{1}{7}$ 
D)  $-\frac{1}{6}$

Question 17

Find the power of $i$.
-$\mathrm{i}^{22}$

Accepted Answer

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

Question 18

Choose the one alternative that best completes the statement or answers the question.
Solve the equation
-$\sqrt[3]{4+6 t}-\sqrt[3]{1-8 t}=0$

Accepted Answer

A)  $\left\{-\frac{3}{14}\right\}$ 
B)  $\left\{\frac{3}{14}\right\}$ 
C)  $\left\{-\frac{14}{3}\right\}$ 
D)  $\left\{\frac{14}{3}\right\}$ 
A)  $\left\{-\frac{3}{14}\right\}$ 
B)  $\left\{\frac{3}{14}\right\}$ 
C)  $\left\{-\frac{14}{3}\right\}$ 
D)  $\left\{\frac{14}{3}\right\}$

Question 19

Perform the indicated operation. Give answer in standard form.
-$(6+8 \mathrm{i})(9+7 \mathrm{i})$

Accepted Answer

A)  $56 \mathrm{i}^{2}+114 \mathrm{i}+54$ 
B)  $-2-114 \mathrm{i}$ 
C)  $-2+114 i$ 
D)  $110+30 \mathrm{i}$ 
A)  $56 \mathrm{i}^{2}+114 \mathrm{i}+54$ 
B)  $-2-114 \mathrm{i}$ 
C)  $-2+114 i$ 
D)  $110+30 \mathrm{i}$

Question 20

Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero.
-$\frac{4}{6-\sqrt{3}}$

Accepted Answer

A)  $\frac{24+4 \sqrt{3}}{33}$ 
B)  $\frac{24+4 \sqrt{3}}{3}$ 
C)  $\frac{4}{6}-\frac{4}{\sqrt{3}}$ 
D)  $\frac{24-4 \sqrt{3}}{33}$ 
A)  $\frac{24+4 \sqrt{3}}{33}$ 
B)  $\frac{24+4 \sqrt{3}}{3}$ 
C)  $\frac{4}{6}-\frac{4}{\sqrt{3}}$ 
D)  $\frac{24-4 \sqrt{3}}{33}$

Choose the one alternative that best completes the statement or answers the question. Multiply using the product rule. - $\sqrt{5} \cdot \sqrt{3}$

Simplify by first writing the radicals with the same index. Then multiply. - $\sqrt{5} \cdot \sqrt[5]{4}$

$\sqrt{9} \cdot \sqrt{25}=\sqrt{9 \cdot 25}$

A manufacturer's cost is given by $C=200 \sqrt[3]{n}+1100$ , where $C$ is the cost and $n$ is the number of parts produced. Find the cost when 729 parts are produced.

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt{-864}$

Simplify by first writing the radicals with the same index. Then multiply. - $\sqrt[3]{6} \cdot \sqrt[4]{2}$

If $n$ is a positive integer, does $\sqrt[n]{x^{n}}=x$ ? Explain.

Simplify the expression involving rational exponents. - $1444^{1 / 2}$

The easiest way to simplify the expression $\sqrt[3]{\frac{2}{9}}$ is to multiply both the numerator and denominator of $\frac{\sqrt[3]{2}}{\sqrt[3]{9}}$ by $\sqrt[3]{9}$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $5 \sqrt{11}+8 \sqrt{11}$

Graph the circle. Identify the center. - $(x-1)^{2}+(y-2)^{2}=4$ $Graph the circle. Identify the center. - (x-1)^{2}+(y-2)^{2}=4$

Find the equation of a circle satisfying the given conditions. -Center: $(0,-7)$ ; radius: $\sqrt{7}$

Write the expression in lowest terms. Assume that all variables represent positive real numbers. - $\frac{6 z+\sqrt{24 z^{3}}}{3 z}$

Explain why the expression cannot be simplified further. $\sqrt[11]{\mathrm{a}}-\sqrt[10]{\mathrm{a}}$

Simplify the expression involving rational exponents. - $216^{-1 / 3}$

Find the power of $i$ . - $\mathrm{i}^{22}$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt[3]{4+6 t}-\sqrt[3]{1-8 t}=0$

Perform the indicated operation. Give answer in standard form. - $(6+8 \mathrm{i})(9+7 \mathrm{i})$

Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero. - $\frac{4}{6-\sqrt{3}}$

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

Choose the one alternative that best completes the statement or answers the question. Multiply using the product rule. - 5⋅3\sqrt{5} \cdot \sqrt{3}5​⋅3​

Simplify by first writing the radicals with the same index. Then multiply. - 5⋅45\sqrt{5} \cdot \sqrt[5]{4}5​⋅54​

9⋅25=9⋅25\sqrt{9} \cdot \sqrt{25}=\sqrt{9 \cdot 25}9​⋅25​=9⋅25​

A manufacturer's cost is given by C=200n3+1100C=200 \sqrt[3]{n}+1100C=2003n​+1100 , where CCC is the cost and nnn is the number of parts produced. Find the cost when 729 parts are produced.

Express the radical in simplified form.Assume that all variables represent positive real numbers. - −864\sqrt{-864}−864​

Simplify by first writing the radicals with the same index. Then multiply. - 63⋅24\sqrt[3]{6} \cdot \sqrt[4]{2}36​⋅42​

If nnn is a positive integer, does xnn=x\sqrt[n]{x^{n}}=xnxn​=x ? Explain.

Simplify the expression involving rational exponents. - 14441/21444^{1 / 2}14441/2

The easiest way to simplify the expression 293\sqrt[3]{\frac{2}{9}}392​​ is to multiply both the numerator and denominator of 2393\frac{\sqrt[3]{2}}{\sqrt[3]{9}}39​32​​ by 93\sqrt[3]{9}39​

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - 511+8115 \sqrt{11}+8 \sqrt{11}511​+811​

Graph the circle. Identify the center. - (x−1)2+(y−2)2=4(x-1)^{2}+(y-2)^{2}=4(x−1)2+(y−2)2=4

Find the equation of a circle satisfying the given conditions. -Center: (0,−7)(0,-7)(0,−7) ; radius: 7\sqrt{7}7​

Write the expression in lowest terms. Assume that all variables represent positive real numbers. - 6z+24z33z\frac{6 z+\sqrt{24 z^{3}}}{3 z}3z6z+24z3​​

Explain why the expression cannot be simplified further. a11−a10\sqrt[11]{\mathrm{a}}-\sqrt[10]{\mathrm{a}}11a​−10a​

Simplify the expression involving rational exponents. - 216−1/3216^{-1 / 3}216−1/3

Find the power of iii . - i22\mathrm{i}^{22}i22

Choose the one alternative that best completes the statement or answers the question. Solve the equation - 4+6t3−1−8t3=0\sqrt[3]{4+6 t}-\sqrt[3]{1-8 t}=034+6t​−31−8t​=0

Perform the indicated operation. Give answer in standard form. - (6+8i)(9+7i)(6+8 \mathrm{i})(9+7 \mathrm{i})(6+8i)(9+7i)

Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero. - 46−3\frac{4}{6-\sqrt{3}}6−3​4​

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

Choose the one alternative that best completes the statement or answers the question. Multiply using the product rule. - $\sqrt{5} \cdot \sqrt{3}$

Simplify by first writing the radicals with the same index. Then multiply. - $\sqrt{5} \cdot \sqrt[5]{4}$

$\sqrt{9} \cdot \sqrt{25}=\sqrt{9 \cdot 25}$

A manufacturer's cost is given by $C=200 \sqrt[3]{n}+1100$ , where $C$ is the cost and $n$ is the number of parts produced. Find the cost when 729 parts are produced.

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt{-864}$

Simplify by first writing the radicals with the same index. Then multiply. - $\sqrt[3]{6} \cdot \sqrt[4]{2}$

If $n$ is a positive integer, does $\sqrt[n]{x^{n}}=x$ ? Explain.

Simplify the expression involving rational exponents. - $1444^{1 / 2}$

The easiest way to simplify the expression $\sqrt[3]{\frac{2}{9}}$ is to multiply both the numerator and denominator of $\frac{\sqrt[3]{2}}{\sqrt[3]{9}}$ by $\sqrt[3]{9}$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $5 \sqrt{11}+8 \sqrt{11}$

Graph the circle. Identify the center. - $(x-1)^{2}+(y-2)^{2}=4$ $Graph the circle. Identify the center. - (x-1)^{2}+(y-2)^{2}=4$

Find the equation of a circle satisfying the given conditions. -Center: $(0,-7)$ ; radius: $\sqrt{7}$

Write the expression in lowest terms. Assume that all variables represent positive real numbers. - $\frac{6 z+\sqrt{24 z^{3}}}{3 z}$

Explain why the expression cannot be simplified further. $\sqrt[11]{\mathrm{a}}-\sqrt[10]{\mathrm{a}}$

Simplify the expression involving rational exponents. - $216^{-1 / 3}$

Find the power of $i$ . - $\mathrm{i}^{22}$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt[3]{4+6 t}-\sqrt[3]{1-8 t}=0$

Perform the indicated operation. Give answer in standard form. - $(6+8 \mathrm{i})(9+7 \mathrm{i})$

Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero. - $\frac{4}{6-\sqrt{3}}$