Question 1

Graph the circle.
-$x^{2}+(y-2)^{2}=36$

Accepted Answer

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

Question 2

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.
-$\sqrt{z^{10}}$

Accepted Answer

A)  $z^{5}$ 
B)  $\frac{z}{2}$ 
C)  $z^{20}$ 
D)  $2 \mathrm{z}$ 
A)  $z^{5}$ 
B)  $\frac{z}{2}$ 
C)  $z^{20}$ 
D)  $2 \mathrm{z}$

Question 3

Perform the indicated operation. Give answer in standard form.
-$\frac{11+i}{1-i}$

Accepted Answer

A)  $6+6 \mathrm{i}$ 
B)  $5+6 \mathrm{i}$ 
C)  $5+12 \mathrm{i}$ 
D)  $5+5 \mathrm{i}$ 
A)  $6+6 \mathrm{i}$ 
B)  $5+6 \mathrm{i}$ 
C)  $5+12 \mathrm{i}$ 
D)  $5+5 \mathrm{i}$

Question 4

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

Accepted Answer

A)  3 
B)  $\frac{3 \sqrt{p+q}}{p+q}$ 
C)  $3 \sqrt{p+q}$ 
D)  $\frac{3}{p+q}$ 
A)  3 
B)  $\frac{3 \sqrt{p+q}}{p+q}$ 
C)  $3 \sqrt{p+q}$ 
D)  $\frac{3}{p+q}$

Question 5

Rationalize the denominator. Assume that all variables represent positive real numbers. 
-$\frac{9 \sqrt{29 \mathrm{x}}}{\sqrt{\mathrm{x}^{3}}}$

Accepted Answer

A)  $\frac{9 \sqrt{29}}{x}$ 
B)  $\frac{261}{x}$ 
C)  $\frac{9 \sqrt{29 x}}{x}$ 
D)  $9 x \sqrt{29}$ 
A)  $\frac{9 \sqrt{29}}{x}$ 
B)  $\frac{261}{x}$ 
C)  $\frac{9 \sqrt{29 x}}{x}$ 
D)  $9 x \sqrt{29}$

Question 6

Find the unknown length in the right triangle. Simplify the answer if necessary.
-

Accepted Answer

A)  $4 \sqrt{5}$ 
B)  $4 \sqrt{3}$ 
C)  $2 \sqrt{3}$ 
D)  $2 \sqrt{5}$ 
A)  $4 \sqrt{5}$ 
B)  $4 \sqrt{3}$ 
C)  $2 \sqrt{3}$ 
D)  $2 \sqrt{5}$

Question 7

Choose the one alternative that best completes the statement or answers the question.
Simplify. Assume that all variables represent positive real numbers.
-$\sqrt{225}+\sqrt{36}$

Accepted Answer

A)  10.5 
B)  21 
C)  $\sqrt{21}$ 
D)  $3 \sqrt{29}$ 
A)  10.5 
B)  21 
C)  $\sqrt{21}$ 
D)  $3 \sqrt{29}$

Question 8

If $a \neq 0, \frac{1}{\mathrm{a}}$ is called the reciprocal of a. Use this definition to express the reciprocal of $6-5 \mathrm{i}$ in the form $a+b i$.

Accepted Answer

The answer of If $a \neq 0, \frac{1}{\mathrm{a}}$ is called...

Question 9

Solve the formula for the indicated variable.
-$L=\sqrt{\frac{2 W}{k}}$ for $k$

Accepted Answer

A)  $k=\frac{2 W}{L}$ 
B)  $k=\frac{2 W}{L^{2}}$ 
C)  $k=2 W^{2}$ 
D)  $k=\frac{4 W^{2}}{L^{2}}$ 
A)  $k=\frac{2 W}{L}$ 
B)  $k=\frac{2 W}{L^{2}}$ 
C)  $k=2 W^{2}$ 
D)  $k=\frac{4 W^{2}}{L^{2}}$

Question 10

Find the unknown length in the right triangle. Simplify the answer if necessary.
-

Accepted Answer

A)  $2 \sqrt{7}$ 
B)  20 
C)  $4 \sqrt{7}$ 
D)  14 
A)  $2 \sqrt{7}$ 
B)  20 
C)  $4 \sqrt{7}$ 
D)  14

Question 11

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.
-$\frac{x^{3 / 5}}{x^{6 / 5} \cdot x^{-5}}$

Accepted Answer

A)  $x^{34 / 5}$ 
B)  $x^{22 / 5}$ 
C)  $\frac{1}{x^{22 / 5}}$ 
D)  $\frac{1}{x^{34 / 5}}$ 
A)  $x^{34 / 5}$ 
B)  $x^{22 / 5}$ 
C)  $\frac{1}{x^{22 / 5}}$ 
D)  $\frac{1}{x^{34 / 5}}$

Question 12

Simplify the root.
-$-\sqrt{x^{12}}$

Accepted Answer

A)  $-\left|x^{6}\right|$ 
B)  $x^{6}$ 
C) $-x^6$ 
D) $ \left|-x^{6}\right| $ 
A)  $-\left|x^{6}\right|$ 
B)  $x^{6}$ 
C) $-x^6$ 
D) $ \left|-x^{6}\right| $

Question 13

Provide an appropriate response.
-$\mathrm{i}=-1$

Accepted Answer

A) True 
 B)False

Question 14

Find the distance between the pair of points.
-$(7,2)$ and $(-1,-3)$

Accepted Answer

A)  $\sqrt{39}$ 
B)  1 
C)  40 
D)  $\sqrt{89}$ 
A)  $\sqrt{39}$ 
B)  1 
C)  40 
D)  $\sqrt{89}$

Question 15

Rationalize the numerator. Assume that all variables represent positive real numbers.
-$\frac{\sqrt{5 x}+2}{7}$

Accepted Answer

A)  $\frac{5 x-4}{7(\sqrt{5 x}+2)}$ 
B)  $\frac{5 x-2}{7(\sqrt{5 x}+2)}$ 
C)  $\frac{5 x-2}{7(\sqrt{5 x}-2)}$ 
D)  $\frac{5 x-4}{7(\sqrt{5 x}-2)}$ 
A)  $\frac{5 x-4}{7(\sqrt{5 x}+2)}$ 
B)  $\frac{5 x-2}{7(\sqrt{5 x}+2)}$ 
C)  $\frac{5 x-2}{7(\sqrt{5 x}-2)}$ 
D)  $\frac{5 x-4}{7(\sqrt{5 x}-2)}$

Question 16

Simplify the radical. Assume that all variables represent positive real numbers.
-$\sqrt[4]{80^{2}}$

Accepted Answer

A)  $4+\sqrt{5}$ 
B)  80 
C)  $\sqrt{80}$ 
D)  $4 \sqrt{5}$ 
A)  $4+\sqrt{5}$ 
B)  80 
C)  $\sqrt{80}$ 
D)  $4 \sqrt{5}$

Question 17

Write with radicals. Assume that all variables represent positive real numbers
-$9^{1 / 2}$

Accepted Answer

A)  $\sqrt{9}$ 
B)  4.5 
C)  $\sqrt{3}$ 
D)  3 
A)  $\sqrt{9}$ 
B)  4.5 
C)  $\sqrt{3}$ 
D)  3

Question 18

Graph the function and give its domain and its range.
-$f(x)=\sqrt[3]{x+3}$

Accepted Answer

A)  $ (-\infty, \infty) ;[3, \infty) $
  
B)  $ (-\infty, \infty) ;(-\infty, \infty) $
  
C)  $ (-\infty, \infty) ;[-3, \infty) $
  
D)  $ (-\infty, \infty) ;(3, \infty) $
  
A)  $ (-\infty, \infty) ;[3, \infty) $
  
B)  $ (-\infty, \infty) ;(-\infty, \infty) $
  
C)  $ (-\infty, \infty) ;[-3, \infty) $
  
D)  $ (-\infty, \infty) ;(3, \infty) $

Question 19

Simplify. Assume that all variables represent positive real numbers.
-$\sqrt[3]{\frac{7}{9 x^{2}}}$

Accepted Answer

A)  $\frac{\sqrt[3]{21 x}}{3 x}$ 
B)  $\frac{\sqrt[3]{567 x^{2}}}{9 x}$ 
C)  $\frac{\sqrt[3]{567 x}}{81}$ 
D)  $\frac{\sqrt[3]{63 x}}{9 x}$ 
A)  $\frac{\sqrt[3]{21 x}}{3 x}$ 
B)  $\frac{\sqrt[3]{567 x^{2}}}{9 x}$ 
C)  $\frac{\sqrt[3]{567 x}}{81}$ 
D)  $\frac{\sqrt[3]{63 x}}{9 x}$

Question 20

Rationalize the numerator. Assume that all variables represent positive real numbers.
-$\frac{2+\sqrt{5}}{6}$

Accepted Answer

A)  $\frac{23}{12-6 \sqrt{5}}$ 
B)  $\frac{-1}{12-2 \sqrt{5}}$ 
C)  $\frac{23}{12-2 \sqrt{5}}$ 
D)  $\frac{-1}{12-6 \sqrt{5}}$ 
A)  $\frac{23}{12-6 \sqrt{5}}$ 
B)  $\frac{-1}{12-2 \sqrt{5}}$ 
C)  $\frac{23}{12-2 \sqrt{5}}$ 
D)  $\frac{-1}{12-6 \sqrt{5}}$

Graph the circle. - $x^{2}+(y-2)^{2}=36$ $Graph the circle. - x^{2}+(y-2)^{2}=36$

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - $\sqrt{z^{10}}$

Perform the indicated operation. Give answer in standard form. - $\frac{11+i}{1-i}$

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

Rationalize the denominator. Assume that all variables represent positive real numbers. - $\frac{9 \sqrt{29 \mathrm{x}}}{\sqrt{\mathrm{x}^{3}}}$

Find the unknown length in the right triangle. Simplify the answer if necessary. -

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $\sqrt{225}+\sqrt{36}$

If $a \neq 0, \frac{1}{\mathrm{a}}$ is called the reciprocal of a. Use this definition to express the reciprocal of $6-5 \mathrm{i}$ in the form $a+b i$ .

Solve the formula for the indicated variable. - $L=\sqrt{\frac{2 W}{k}}$ for $k$

Find the unknown length in the right triangle. Simplify the answer if necessary. -

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $\frac{x^{3 / 5}}{x^{6 / 5} \cdot x^{-5}}$

Simplify the root. - $-\sqrt{x^{12}}$

Provide an appropriate response. - $\mathrm{i}=-1$

Find the distance between the pair of points. - $(7,2)$ and $(-1,-3)$

Rationalize the numerator. Assume that all variables represent positive real numbers. - $\frac{\sqrt{5 x}+2}{7}$

Simplify the radical. Assume that all variables represent positive real numbers. - $\sqrt[4]{80^{2}}$

Write with radicals. Assume that all variables represent positive real numbers - $9^{1 / 2}$

Graph the function and give its domain and its range. - $f(x)=\sqrt[3]{x+3}$ $Graph the function and give its domain and its range. - f(x)=\sqrt[3]{x+3}$

Simplify. Assume that all variables represent positive real numbers. - $\sqrt[3]{\frac{7}{9 x^{2}}}$

Rationalize the numerator. Assume that all variables represent positive real numbers. - $\frac{2+\sqrt{5}}{6}$

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

Graph the circle. - x2+(y−2)2=36x^{2}+(y-2)^{2}=36x2+(y−2)2=36

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - z10\sqrt{z^{10}}z10​

Perform the indicated operation. Give answer in standard form. - 11+i1−i\frac{11+i}{1-i}1−i11+i​

Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero. - 3p+q\frac{3}{\sqrt{\mathrm{p}+\mathrm{q}}}p+q​3​

Rationalize the denominator. Assume that all variables represent positive real numbers. - 929xx3\frac{9 \sqrt{29 \mathrm{x}}}{\sqrt{\mathrm{x}^{3}}}x3​929x​​

Find the unknown length in the right triangle. Simplify the answer if necessary. -

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - 225+36\sqrt{225}+\sqrt{36}225​+36​

If a≠0,1aa \neq 0, \frac{1}{\mathrm{a}}a=0,a1​ is called the reciprocal of a. Use this definition to express the reciprocal of 6−5i6-5 \mathrm{i}6−5i in the form a+bia+b ia+bi .

Solve the formula for the indicated variable. - L=2WkL=\sqrt{\frac{2 W}{k}}L=k2W​​ for kkk

Find the unknown length in the right triangle. Simplify the answer if necessary. -

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - x3/5x6/5⋅x−5\frac{x^{3 / 5}}{x^{6 / 5} \cdot x^{-5}}x6/5⋅x−5x3/5​

Simplify the root. - −x12-\sqrt{x^{12}}−x12​

Provide an appropriate response. - i=−1\mathrm{i}=-1i=−1

Find the distance between the pair of points. - (7,2)(7,2)(7,2) and (−1,−3)(-1,-3)(−1,−3)

Rationalize the numerator. Assume that all variables represent positive real numbers. - 5x+27\frac{\sqrt{5 x}+2}{7}75x​+2​

Simplify the radical. Assume that all variables represent positive real numbers. - 8024\sqrt[4]{80^{2}}4802​

Write with radicals. Assume that all variables represent positive real numbers - 91/29^{1 / 2}91/2

Graph the function and give its domain and its range. - f(x)=x+33f(x)=\sqrt[3]{x+3}f(x)=3x+3​

Simplify. Assume that all variables represent positive real numbers. - 79x23\sqrt[3]{\frac{7}{9 x^{2}}}39x27​​

Rationalize the numerator. Assume that all variables represent positive real numbers. - 2+56\frac{2+\sqrt{5}}{6}62+5​​

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

Graph the circle. - $x^{2}+(y-2)^{2}=36$ $Graph the circle. - x^{2}+(y-2)^{2}=36$

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - $\sqrt{z^{10}}$

Perform the indicated operation. Give answer in standard form. - $\frac{11+i}{1-i}$

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

Rationalize the denominator. Assume that all variables represent positive real numbers. - $\frac{9 \sqrt{29 \mathrm{x}}}{\sqrt{\mathrm{x}^{3}}}$

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $\sqrt{225}+\sqrt{36}$

If $a \neq 0, \frac{1}{\mathrm{a}}$ is called the reciprocal of a. Use this definition to express the reciprocal of $6-5 \mathrm{i}$ in the form $a+b i$ .

Solve the formula for the indicated variable. - $L=\sqrt{\frac{2 W}{k}}$ for $k$

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $\frac{x^{3 / 5}}{x^{6 / 5} \cdot x^{-5}}$

Simplify the root. - $-\sqrt{x^{12}}$

Provide an appropriate response. - $\mathrm{i}=-1$

Find the distance between the pair of points. - $(7,2)$ and $(-1,-3)$

Rationalize the numerator. Assume that all variables represent positive real numbers. - $\frac{\sqrt{5 x}+2}{7}$

Simplify the radical. Assume that all variables represent positive real numbers. - $\sqrt[4]{80^{2}}$

Write with radicals. Assume that all variables represent positive real numbers - $9^{1 / 2}$

Graph the function and give its domain and its range. - $f(x)=\sqrt[3]{x+3}$ $Graph the function and give its domain and its range. - f(x)=\sqrt[3]{x+3}$

Simplify. Assume that all variables represent positive real numbers. - $\sqrt[3]{\frac{7}{9 x^{2}}}$

Rationalize the numerator. Assume that all variables represent positive real numbers. - $\frac{2+\sqrt{5}}{6}$