Question 1

Multiply or divide as indicated.
-$\frac{\sqrt{-72}}{\sqrt{-36}}$

Accepted Answer

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

Question 2

A formula for calculating the distance, $d$, one can see from an airplane to the horizon on a clear day is $d=1.22 x^{1 / 2}$, where $x$ is the altitude of the plane in feet and $d$ is given in miles. How far can one see in a plane flying at 25,000 feet? Round your answer to the nearest tenth mile, if necessary.

Accepted Answer

A)  192.9 miles 
B)  174.6 miles 
C)  1525 miles 
D)  15,250 miles 
A)  192.9 miles 
B)  174.6 miles 
C)  1525 miles 
D)  15,250 miles A

Question 3

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.
-$\sqrt{\frac{81}{16}}$

Accepted Answer

A)  $\frac{9}{4}$ 
B)  $\frac{5}{2}$ 
C)  5 
D)  $\frac{9}{5}$ 
A)  $\frac{9}{4}$ 
B)  $\frac{5}{2}$ 
C)  5 
D)  $\frac{9}{5}$ A

Question 4

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

Accepted Answer

A)  $x^{13 / 3}$ 
B)  $\frac{1}{x^{13 / 3}}$ 
C)  $\frac{1}{x^{17 / 3}}$ 
D)  $x^{17 / 3}$ 
A)  $x^{13 / 3}$ 
B)  $\frac{1}{x^{13 / 3}}$ 
C)  $\frac{1}{x^{17 / 3}}$ 
D)  $x^{17 / 3}$

Question 5

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

Accepted Answer

A)  $\sqrt{5}+\sqrt{10}$ 
B)  $\sqrt{35}$ 
C)  15 
D)  $5+\sqrt{10}$ 
A)  $\sqrt{5}+\sqrt{10}$ 
B)  $\sqrt{35}$ 
C)  15 
D)  $5+\sqrt{10}$

Question 6

Find the decimal approximation for the radical. Round the answer to three decimal places.
-$-\sqrt{23}$

Accepted Answer

A)  -4.796 
B)  -23.000 
C)  -4.801 
D)  -4.793 
A)  -4.796 
B)  -23.000 
C)  -4.801 
D)  -4.793

Question 7

Write with radicals. Assume that all variables represent positive real numbers.
-$(\mathrm{mn})^{1 / 6}$

Accepted Answer

A)  $\frac{1}{\sqrt[6]{m n}}$ 
B)  $(\sqrt{m n})^{6}$ 
C)  $\sqrt[6]{m n}$ 
D)  $(\mathrm{mn})^{-6}$ 
A)  $\frac{1}{\sqrt[6]{m n}}$ 
B)  $(\sqrt{m n})^{6}$ 
C)  $\sqrt[6]{m n}$ 
D)  $(\mathrm{mn})^{-6}$

Question 8

Choose the one alternative that best completes the statement or answers the question.
Evaluate
-$\sqrt[3]{-8}$

Accepted Answer

A)  -2 
B)  -4 
C)  2 
D)  4 
A)  -2 
B)  -4 
C)  2 
D)  4

Question 9

Multiply, then simplify the product. Assume that all variables represent positive real numbers.
-$(4+\sqrt[3]{3})(4-\sqrt[3]{3})$

Accepted Answer

A)  7 
B)  13 
C)  $16-\sqrt[3]{9}$ 
D)  $16-\sqrt[3]{3}$ 
A)  7 
B)  13 
C)  $16-\sqrt[3]{9}$ 
D)  $16-\sqrt[3]{3}$

Question 10

What is wrong with this? $\left(2 x^{3}\right)^{-1}=2 x^{-3}$

Accepted Answer

The exponent was not

Question 11

Rationalize the numerator. Assume that all variables represent positive real numbers.
-$\frac{\sqrt{3 x}-4}{10}$

Accepted Answer

A)  $\frac{3 x-4}{10(\sqrt{3 x}-4)}$ 
B)  $\frac{3 x-16}{10(\sqrt{3 x}+4)}$ 
C)  $\frac{3 x-4}{10(\sqrt{3 x}+4)}$ 
D)  $\frac{3 x-16}{10(\sqrt{3 x}-4)}$ 
A)  $\frac{3 x-4}{10(\sqrt{3 x}-4)}$ 
B)  $\frac{3 x-16}{10(\sqrt{3 x}+4)}$ 
C)  $\frac{3 x-4}{10(\sqrt{3 x}+4)}$ 
D)  $\frac{3 x-16}{10(\sqrt{3 x}-4)}$

Question 12

Choose the one alternative that best completes the statement or answers the question.
Simplify. Assume that all variables represent positive real numbers.
-$\sqrt{\frac{5}{6}}-\sqrt{\frac{45}{54}}$

Accepted Answer

A)  0 
B)  -3 
C)  $-\frac{1}{3}$ 
D)  -1 
A)  0 
B)  -3 
C)  $-\frac{1}{3}$ 
D)  -1

Question 13

Solve the formula for the indicated variable.
-$r=\sqrt{\frac{S}{4 \pi}}$ for $S$

Accepted Answer

A)  $S=\frac{r^{2}}{4 \pi}$ 
B)  $S=4 \pi r^{2}$ 
C)  $S=16 \pi^{2} r^{2}$ 
D)  $S=4 \pi r$ 
A)  $S=\frac{r^{2}}{4 \pi}$ 
B)  $S=4 \pi r^{2}$ 
C)  $S=16 \pi^{2} r^{2}$ 
D)  $S=4 \pi r$

Question 14

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.
-$\sqrt[4]{1296}$

Accepted Answer

A)  6 
B)  36 
C)  7 
D)  5 
A)  6 
B)  36 
C)  7 
D)  5

Question 15

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.
-$x^{1 / 7} \cdot x^{6 / 7}$

Accepted Answer

A)  $\frac{1}{x}$ 
B)  $x^{6 / 49}$ 
C)  $x$ 
D)  $x^{6 / 7}$ 
A)  $\frac{1}{x}$ 
B)  $x^{6 / 49}$ 
C)  $x$ 
D)  $x^{6 / 7}$

Question 16

Choose the one alternative that best completes the statement or answers the question.
Simplify. Assume that all variables represent positive real numbers.
-$5 \sqrt[9]{x^{10} y}-4 x \sqrt[9]{x y}$

Accepted Answer

A)  $x \sqrt[9]{x y}$ 
B)  $(5-4 x) \sqrt[9]{x y}$ 
C)  Cannot be simplified 
D)  $2 x \sqrt[9]{x y}$ 
A)  $x \sqrt[9]{x y}$ 
B)  $(5-4 x) \sqrt[9]{x y}$ 
C)  Cannot be simplified 
D)  $2 x \sqrt[9]{x y}$

Question 17

Find the equation of a circle satisfying the given conditions.
-Center: $(-6,10)$; radius: $\sqrt{7}$

Accepted Answer

A)  $(x-6)^{2}+(y+10)^{2}=7$ 
B)  $(x+10)^{2}+(y-6)^{2}=49$ 
C)  $(x+6)^{2}+(y-10)^{2}=7$ 
D)  $(x-10)^{2}+(y+6)^{2}=49$ 
A)  $(x-6)^{2}+(y+10)^{2}=7$ 
B)  $(x+10)^{2}+(y-6)^{2}=49$ 
C)  $(x+6)^{2}+(y-10)^{2}=7$ 
D)  $(x-10)^{2}+(y+6)^{2}=49$

Question 18

Solve the equation.
-$\sqrt[3]{10 x}=\sqrt[3]{7 x-9}$

Accepted Answer

A)  $\{-27\}$ 
B)  $\{-3\}$ 
C)  $\varnothing$ 
D)  $\{3\}$ 
A)  $\{-27\}$ 
B)  $\{-3\}$ 
C)  $\varnothing$ 
D)  $\{3\}$

Question 19

Express the radical in simplified form.Assume that all variables represent positive real numbers.
-$-\sqrt{405 k^{7} q^{8}}$

Accepted Answer

A)  $9 \mathrm{k}^{7} \mathrm{q}^{8} \sqrt{5 \mathrm{k}}$ 
B)  $-9 k^{3} q^{4} \sqrt{5 k}$ 
C)  $-9 \mathrm{k}^{3} \mathrm{q}^{4} \sqrt{5}$ 
D)  $9 \mathrm{k}^{3} \mathrm{q}^{4} \sqrt{5 \mathrm{k}}$ 
A)  $9 \mathrm{k}^{7} \mathrm{q}^{8} \sqrt{5 \mathrm{k}}$ 
B)  $-9 k^{3} q^{4} \sqrt{5 k}$ 
C)  $-9 \mathrm{k}^{3} \mathrm{q}^{4} \sqrt{5}$ 
D)  $9 \mathrm{k}^{3} \mathrm{q}^{4} \sqrt{5 \mathrm{k}}$

Question 20

Tell whether the statement is true or false. If it is false, give the correct answer. Explain.
$\sqrt[3]{x} \cdot \sqrt[3]{x}=x$

Accepted Answer

A) True 
 B)False

Multiply or divide as indicated. - $\frac{\sqrt{-72}}{\sqrt{-36}}$

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $\sqrt{\frac{81}{16}}$

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

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

Find the decimal approximation for the radical. Round the answer to three decimal places. - $-\sqrt{23}$

Write with radicals. Assume that all variables represent positive real numbers. - $(\mathrm{mn})^{1 / 6}$

Choose the one alternative that best completes the statement or answers the question. Evaluate - $\sqrt[3]{-8}$

Multiply, then simplify the product. Assume that all variables represent positive real numbers. - $(4+\sqrt[3]{3})(4-\sqrt[3]{3})$

What is wrong with this? $\left(2 x^{3}\right)^{-1}=2 x^{-3}$

Rationalize the numerator. Assume that all variables represent positive real numbers. - $\frac{\sqrt{3 x}-4}{10}$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $\sqrt{\frac{5}{6}}-\sqrt{\frac{45}{54}}$

Solve the formula for the indicated variable. - $r=\sqrt{\frac{S}{4 \pi}}$ for $S$

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $\sqrt[4]{1296}$

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $x^{1 / 7} \cdot x^{6 / 7}$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $5 \sqrt[9]{x^{10} y}-4 x \sqrt[9]{x y}$

Find the equation of a circle satisfying the given conditions. -Center: $(-6,10)$ ; radius: $\sqrt{7}$

Solve the equation. - $\sqrt[3]{10 x}=\sqrt[3]{7 x-9}$

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $-\sqrt{405 k^{7} q^{8}}$

Tell whether the statement is true or false. If it is false, give the correct answer. Explain. $\sqrt[3]{x} \cdot \sqrt[3]{x}=x$

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

Multiply or divide as indicated. - −72−36\frac{\sqrt{-72}}{\sqrt{-36}}−36​−72​​

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - 8116\sqrt{\frac{81}{16}}1681​​

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

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

Find the decimal approximation for the radical. Round the answer to three decimal places. - −23-\sqrt{23}−23​

Write with radicals. Assume that all variables represent positive real numbers. - (mn)1/6(\mathrm{mn})^{1 / 6}(mn)1/6

Choose the one alternative that best completes the statement or answers the question. Evaluate - −83\sqrt[3]{-8}3−8​

Multiply, then simplify the product. Assume that all variables represent positive real numbers. - (4+33)(4−33)(4+\sqrt[3]{3})(4-\sqrt[3]{3})(4+33​)(4−33​)

What is wrong with this? (2x3)−1=2x−3\left(2 x^{3}\right)^{-1}=2 x^{-3}(2x3)−1=2x−3

Rationalize the numerator. Assume that all variables represent positive real numbers. - 3x−410\frac{\sqrt{3 x}-4}{10}103x​−4​

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - 56−4554\sqrt{\frac{5}{6}}-\sqrt{\frac{45}{54}}65​​−5445​​

Solve the formula for the indicated variable. - r=S4πr=\sqrt{\frac{S}{4 \pi}}r=4πS​​ for SSS

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - 12964\sqrt[4]{1296}41296​

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - x1/7⋅x6/7x^{1 / 7} \cdot x^{6 / 7}x1/7⋅x6/7

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - 5x10y9−4xxy95 \sqrt[9]{x^{10} y}-4 x \sqrt[9]{x y}59x10y​−4x9xy​

Find the equation of a circle satisfying the given conditions. -Center: (−6,10)(-6,10)(−6,10) ; radius: 7\sqrt{7}7​

Solve the equation. - 10x3=7x−93\sqrt[3]{10 x}=\sqrt[3]{7 x-9}310x​=37x−9​

Express the radical in simplified form.Assume that all variables represent positive real numbers. - −405k7q8-\sqrt{405 k^{7} q^{8}}−405k7q8​

Tell whether the statement is true or false. If it is false, give the correct answer. Explain. x3⋅x3=x\sqrt[3]{x} \cdot \sqrt[3]{x}=x3x​⋅3x​=x

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

Multiply or divide as indicated. - $\frac{\sqrt{-72}}{\sqrt{-36}}$

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $\sqrt{\frac{81}{16}}$

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

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

Find the decimal approximation for the radical. Round the answer to three decimal places. - $-\sqrt{23}$

Write with radicals. Assume that all variables represent positive real numbers. - $(\mathrm{mn})^{1 / 6}$

Choose the one alternative that best completes the statement or answers the question. Evaluate - $\sqrt[3]{-8}$

Multiply, then simplify the product. Assume that all variables represent positive real numbers. - $(4+\sqrt[3]{3})(4-\sqrt[3]{3})$

What is wrong with this? $\left(2 x^{3}\right)^{-1}=2 x^{-3}$

Rationalize the numerator. Assume that all variables represent positive real numbers. - $\frac{\sqrt{3 x}-4}{10}$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $\sqrt{\frac{5}{6}}-\sqrt{\frac{45}{54}}$

Solve the formula for the indicated variable. - $r=\sqrt{\frac{S}{4 \pi}}$ for $S$

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $\sqrt[4]{1296}$

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $x^{1 / 7} \cdot x^{6 / 7}$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $5 \sqrt[9]{x^{10} y}-4 x \sqrt[9]{x y}$

Find the equation of a circle satisfying the given conditions. -Center: $(-6,10)$ ; radius: $\sqrt{7}$

Solve the equation. - $\sqrt[3]{10 x}=\sqrt[3]{7 x-9}$

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $-\sqrt{405 k^{7} q^{8}}$

Tell whether the statement is true or false. If it is false, give the correct answer. Explain. $\sqrt[3]{x} \cdot \sqrt[3]{x}=x$