Question 1

Find the decimal approximation for the radical. Round the answer to three decimal places.
-$\sqrt[5]{-83}$

Accepted Answer

A)  -2.420 
B)  -2.432 
C)  -2.441 
D)  -2.450 
A)  -2.420 
B)  -2.432 
C)  -2.441 
D)  -2.450

Question 2

If $a<0$, which of the following correctly describes $-\sqrt{-a}$ ?

Accepted Answer

A)  Zero 
B)  Positive 
C)  Negative 
D)  Not a real number 
A)  Zero 
B)  Positive 
C)  Negative 
D)  Not a real number

Question 3

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.
-$\sqrt{441}$

Accepted Answer

A)  Not a real number 
B)  194,481 
C)  $\frac{1}{441}$ 
D)  21 
A)  Not a real number 
B)  194,481 
C)  $\frac{1}{441}$ 
D)  21

Question 4

Write the number as a product of a real number and $i$. Simplify the radical expression.
-$\sqrt{-272}$

Accepted Answer

A)  $4 \mathrm{i} \sqrt{17}$ 
B)  $-4 \sqrt{17}$ 
C)  $-4 \mathrm{i} \sqrt{17}$ 
D)  $4 \sqrt{17}$ 
A)  $4 \mathrm{i} \sqrt{17}$ 
B)  $-4 \sqrt{17}$ 
C)  $-4 \mathrm{i} \sqrt{17}$ 
D)  $4 \sqrt{17}$

Question 5

Write the expression in the form a + bi.
-$\frac{4-4 \mathrm{i}}{5+3 \mathrm{i}}$

Accepted Answer

A)  $\frac{4}{17}-\frac{16}{17} \mathrm{i}$ 
B)  $\frac{32}{17}+\frac{8}{17} \mathrm{i}$ 
C)  $\frac{4}{17}+\frac{16}{17} \mathrm{i}$ 
D)  $-\frac{32}{17}+\frac{8}{17} \mathrm{i}$ 
A)  $\frac{4}{17}-\frac{16}{17} \mathrm{i}$ 
B)  $\frac{32}{17}+\frac{8}{17} \mathrm{i}$ 
C)  $\frac{4}{17}+\frac{16}{17} \mathrm{i}$ 
D)  $-\frac{32}{17}+\frac{8}{17} \mathrm{i}$

Question 6

Suppose a rectangle has length $\sqrt{40}$ and width $\sqrt{79}$. Which of the following is the best estimate of its perimeter?

Accepted Answer

A)  54 
B)  30 
C)  21 
D)  81 
A)  54 
B)  30 
C)  21 
D)  81

Question 7

The principal fifth root of -243 is 3 .

Accepted Answer

A) True 
 B)False

Question 8

Choose the one alternative that best completes the statement or answers the question.
Simplify. Assume that all variables represent positive real numbers.
-$\sqrt{5 x}+7 \sqrt{45 x}+2 \sqrt{20 x}$

Accepted Answer

A)  $25 \sqrt{5 x}$ 
B)  $10 \sqrt{70 x}$ 
C)  $26 \sqrt{5 x}$ 
D)  $9 \sqrt{70 x}$ 
A)  $25 \sqrt{5 x}$ 
B)  $10 \sqrt{70 x}$ 
C)  $26 \sqrt{5 x}$ 
D)  $9 \sqrt{70 x}$

Question 9

Add or subtract as indicated. Write your answer in the form $a+b i$.
-$(3-5 \mathrm{i})+(4+9 \mathrm{i})$

Accepted Answer

A)  $7+4 \mathrm{i}$ 
B)  $-7-4 \mathrm{i}$ 
C)  7 - $4 \mathrm{i}$ 
D)  $-1+14 \mathrm{i}$ 
A)  $7+4 \mathrm{i}$ 
B)  $-7-4 \mathrm{i}$ 
C)  7 - $4 \mathrm{i}$ 
D)  $-1+14 \mathrm{i}$

Question 10

Multiply, then simplify the product. Assume that all variables represent positive real numbers.
-$\sqrt{6}(\sqrt{294}-\sqrt{24})$

Accepted Answer

A)  30 
B)  54 
C)  $36-6 \sqrt{3}$ 
D)  $6 \sqrt{7}-12$ 
A)  30 
B)  54 
C)  $36-6 \sqrt{3}$ 
D)  $6 \sqrt{7}-12$

Question 11

$X_{L}$ is $I=\frac{E}{R+\left(X_{L}-X_{C}\right)}$. . Use this law to solve the problem.
-Find $\mathrm{E}$ if $\mathrm{I}=4+3 i, R=3, X_{L}=8$, and $X_{C}=4$.

Accepted Answer

A)  $57 \mathrm{i}$ 
B)  $25 \mathrm{i}$ 
C)  $-57 \mathrm{i}$ 
D)  $-25 \mathrm{i}$ 
A)  $57 \mathrm{i}$ 
B)  $25 \mathrm{i}$ 
C)  $-57 \mathrm{i}$ 
D)  $-25 \mathrm{i}$

Question 12

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

Accepted Answer

A)  20 
B)  $5 \sqrt{34}$ 
C)  24 
D)  10 
A)  20 
B)  $5 \sqrt{34}$ 
C)  24 
D)  10

Question 13

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.
-$\sqrt{-324}$

Accepted Answer

A)  18 
B)  Not a real number 
C)  104,976 
D)  $\frac{1}{324}$ 
A)  18 
B)  Not a real number 
C)  104,976 
D)  $\frac{1}{324}$

Question 14

Simplify the expression. Assume that all variables represent positive real numbers.
-$\left(\frac{x^{-6} y^{-4}}{x^{-4} y^{5}}\right)^{-3 / 5}$

Accepted Answer

A)  $x^{6 / 5} y^{27 / 5}$ 
B)  $x^{30 / 5} y^{27 / 5}$ 
C)  $x^{6 / 5} y^{12}$ 
D)  $x^{72 / 5} y^{27 / 5}$ 
A)  $x^{6 / 5} y^{27 / 5}$ 
B)  $x^{30 / 5} y^{27 / 5}$ 
C)  $x^{6 / 5} y^{12}$ 
D)  $x^{72 / 5} y^{27 / 5}$

Question 15

Choose the one alternative that best completes the statement or answers the question.
Solve the equation
-$\sqrt{2 \mathrm{k}+1}=13$

Accepted Answer

A)  $\{84\}$ 
B)  $\{-84\}$ 
C)  $\{42\}$ 
D)  $\{168\}$ 
A)  $\{84\}$ 
B)  $\{-84\}$ 
C)  $\{42\}$ 
D)  $\{168\}$

Question 16

Provide an appropriate response.
-If $\mathrm{a}<0$ and $\mathrm{b}<0$, then $\sqrt{\mathrm{a}} \cdot \sqrt{\mathrm{b}}=\sqrt{\mathrm{ab}}$.

Accepted Answer

A) True 
 B)False

Question 17

Choose the one alternative that best completes the statement or answers the question.
Solve the equation
-$\sqrt{\mathrm{x}+6}+\sqrt{2-\mathrm{x}}=4$

Accepted Answer

A)  $\{\sqrt{31},-2\}$ 
B)  $\{-2\}$ 
C)  $\{0\}$ 
D)  $\{2,-2\}$ 
A)  $\{\sqrt{31},-2\}$ 
B)  $\{-2\}$ 
C)  $\{0\}$ 
D)  $\{2,-2\}$

Question 18

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

Accepted Answer

A)  $(-\infty, \infty) ;(-\infty, \infty)$
  
B)  $(-\infty, \infty) ;(-3, \infty)$
  
C)  $(-\infty, \infty) ;[3, \infty)$
  
D)  $(0, \infty) ;(-\infty, \infty)$
  
A)  $(-\infty, \infty) ;(-\infty, \infty)$
  
B)  $(-\infty, \infty) ;(-3, \infty)$
  
C)  $(-\infty, \infty) ;[3, \infty)$
  
D)  $(0, \infty) ;(-\infty, \infty)$

Question 19

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.
-$z^{-2 / 7} \cdot z^{3 / 7}$

Accepted Answer

A)  $z^{1 / 7}$ 
B)  $z^{6 / 7}$ 
C)  $z^{-1 / 7}$ 
D)  $z^{7 / 6}$ 
A)  $z^{1 / 7}$ 
B)  $z^{6 / 7}$ 
C)  $z^{-1 / 7}$ 
D)  $z^{7 / 6}$

Question 20

Simplify the radical. Assume that all variables represent positive real numbers
-$\sqrt[3]{\frac{125}{216}}$

Accepted Answer

A)  30 
B)  $\frac{25}{36}$ 
C)  $\frac{125}{216}$ 
D)  $\frac{5}{6}$ 
A)  30 
B)  $\frac{25}{36}$ 
C)  $\frac{125}{216}$ 
D)  $\frac{5}{6}$

Find the decimal approximation for the radical. Round the answer to three decimal places. - $\sqrt[5]{-83}$

If $a<0$ , which of the following correctly describes $-\sqrt{-a}$ ?

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $\sqrt{441}$

Write the number as a product of a real number and $i$ . Simplify the radical expression. - $\sqrt{-272}$

Write the expression in the form a + bi. - $\frac{4-4 \mathrm{i}}{5+3 \mathrm{i}}$

Suppose a rectangle has length $\sqrt{40}$ and width $\sqrt{79}$ . Which of the following is the best estimate of its perimeter?

The principal fifth root of -243 is 3 .

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $\sqrt{5 x}+7 \sqrt{45 x}+2 \sqrt{20 x}$

Add or subtract as indicated. Write your answer in the form $a+b i$ . - $(3-5 \mathrm{i})+(4+9 \mathrm{i})$

Multiply, then simplify the product. Assume that all variables represent positive real numbers. - $\sqrt{6}(\sqrt{294}-\sqrt{24})$

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. Find the root if it is a real number. - $\sqrt{-324}$

Simplify the expression. Assume that all variables represent positive real numbers. - $\left(\frac{x^{-6} y^{-4}}{x^{-4} y^{5}}\right)^{-3 / 5}$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{2 \mathrm{k}+1}=13$

Provide an appropriate response. -If $\mathrm{a}<0$ and $\mathrm{b}<0$ , then $\sqrt{\mathrm{a}} \cdot \sqrt{\mathrm{b}}=\sqrt{\mathrm{ab}}$ .

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{\mathrm{x}+6}+\sqrt{2-\mathrm{x}}=4$

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

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $z^{-2 / 7} \cdot z^{3 / 7}$

Simplify the radical. Assume that all variables represent positive real numbers - $\sqrt[3]{\frac{125}{216}}$

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

Find the decimal approximation for the radical. Round the answer to three decimal places. - −835\sqrt[5]{-83}5−83​

If a<0a<0a<0 , which of the following correctly describes −−a-\sqrt{-a}−−a​ ?

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - 441\sqrt{441}441​

Write the number as a product of a real number and iii . Simplify the radical expression. - −272\sqrt{-272}−272​

Write the expression in the form a + bi. - 4−4i5+3i\frac{4-4 \mathrm{i}}{5+3 \mathrm{i}}5+3i4−4i​

Suppose a rectangle has length 40\sqrt{40}40​ and width 79\sqrt{79}79​ . Which of the following is the best estimate of its perimeter?

The principal fifth root of -243 is 3 .

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - 5x+745x+220x\sqrt{5 x}+7 \sqrt{45 x}+2 \sqrt{20 x}5x​+745x​+220x​

Add or subtract as indicated. Write your answer in the form a+bia+b ia+bi . - (3−5i)+(4+9i)(3-5 \mathrm{i})+(4+9 \mathrm{i})(3−5i)+(4+9i)

Multiply, then simplify the product. Assume that all variables represent positive real numbers. - 6(294−24)\sqrt{6}(\sqrt{294}-\sqrt{24})6​(294​−24​)

XLX_{L}XL​ is I=ER+(XL−XC)I=\frac{E}{R+\left(X_{L}-X_{C}\right)}I=R+(XL​−XC​)E​ . . Use this law to solve the problem. -Find E\mathrm{E}E if I=4+3i,R=3,XL=8\mathrm{I}=4+3 i, R=3, X_{L}=8I=4+3i,R=3,XL​=8 , and XC=4X_{C}=4XC​=4 .

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. Find the root if it is a real number. - −324\sqrt{-324}−324​

Simplify the expression. Assume that all variables represent positive real numbers. - (x−6y−4x−4y5)−3/5\left(\frac{x^{-6} y^{-4}}{x^{-4} y^{5}}\right)^{-3 / 5}(x−4y5x−6y−4​)−3/5

Choose the one alternative that best completes the statement or answers the question. Solve the equation - 2k+1=13\sqrt{2 \mathrm{k}+1}=132k+1​=13

Provide an appropriate response. -If a<0\mathrm{a}<0a<0 and b<0\mathrm{b}<0b<0 , then a⋅b=ab\sqrt{\mathrm{a}} \cdot \sqrt{\mathrm{b}}=\sqrt{\mathrm{ab}}a​⋅b​=ab​ .

Choose the one alternative that best completes the statement or answers the question. Solve the equation - x+6+2−x=4\sqrt{\mathrm{x}+6}+\sqrt{2-\mathrm{x}}=4x+6​+2−x​=4

Graph the function and give its domain and its range. - f(x)=x3−3f(x)=\sqrt[3]{x}-3f(x)=3x​−3

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - z−2/7⋅z3/7z^{-2 / 7} \cdot z^{3 / 7}z−2/7⋅z3/7

Simplify the radical. Assume that all variables represent positive real numbers - 1252163\sqrt[3]{\frac{125}{216}}3216125​​

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

Find the decimal approximation for the radical. Round the answer to three decimal places. - $\sqrt[5]{-83}$

If $a<0$ , which of the following correctly describes $-\sqrt{-a}$ ?

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $\sqrt{441}$

Write the number as a product of a real number and $i$ . Simplify the radical expression. - $\sqrt{-272}$

Write the expression in the form a + bi. - $\frac{4-4 \mathrm{i}}{5+3 \mathrm{i}}$

Suppose a rectangle has length $\sqrt{40}$ and width $\sqrt{79}$ . Which of the following is the best estimate of its perimeter?

Choose the one alternative that best completes the statement or answers the question. Simplify. Assume that all variables represent positive real numbers. - $\sqrt{5 x}+7 \sqrt{45 x}+2 \sqrt{20 x}$

Add or subtract as indicated. Write your answer in the form $a+b i$ . - $(3-5 \mathrm{i})+(4+9 \mathrm{i})$

Multiply, then simplify the product. Assume that all variables represent positive real numbers. - $\sqrt{6}(\sqrt{294}-\sqrt{24})$

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $\sqrt{-324}$

Simplify the expression. Assume that all variables represent positive real numbers. - $\left(\frac{x^{-6} y^{-4}}{x^{-4} y^{5}}\right)^{-3 / 5}$

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{2 \mathrm{k}+1}=13$

Provide an appropriate response. -If $\mathrm{a}<0$ and $\mathrm{b}<0$ , then $\sqrt{\mathrm{a}} \cdot \sqrt{\mathrm{b}}=\sqrt{\mathrm{ab}}$ .

Choose the one alternative that best completes the statement or answers the question. Solve the equation - $\sqrt{\mathrm{x}+6}+\sqrt{2-\mathrm{x}}=4$

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

Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers. - $z^{-2 / 7} \cdot z^{3 / 7}$

Simplify the radical. Assume that all variables represent positive real numbers - $\sqrt[3]{\frac{125}{216}}$