Question 1

Can the sum be simplified without first simplifying the individual radical expressions? $\sqrt[13]{160}+\sqrt[13]{295,245}$

Accepted Answer

A) True 
 B)False

Question 2

Explain why $\sqrt[3]{-3}$ and $-\sqrt[3]{3}$ represent the same number.

Accepted Answer

Answers wi

Question 3

Express the radical in simplified form.Assume that all variables represent positive real numbers.
-$\sqrt[4]{48}$

Accepted Answer

A)  2 
B)  $2 \sqrt[4]{3}$ 
C)  $3 \sqrt[4]{2}$ 
D)  6 
A)  2 
B)  $2 \sqrt[4]{3}$ 
C)  $3 \sqrt[4]{2}$ 
D)  6

Question 4

$X_{L}$ is $I=\frac{E}{R+\left(X_{L}-X_{C}\right)}$. . Use this law to solve the problem.
-Find $X_{C}$ if $I=6-2 i, E=5-5 i, R=9$, and $X_{L}=1$.

Accepted Answer

A)  $\frac{3}{2}+8 \mathrm{i}$ 
B)  $\frac{3}{2}-8 \mathrm{i}$ 
C)  $-\frac{3}{2}-8 \mathrm{i}$ 
D)  $-\frac{3}{2}+8 \mathrm{i}$ 
A)  $\frac{3}{2}+8 \mathrm{i}$ 
B)  $\frac{3}{2}-8 \mathrm{i}$ 
C)  $-\frac{3}{2}-8 \mathrm{i}$ 
D)  $-\frac{3}{2}+8 \mathrm{i}$

Question 5

Choose the one alternative that best completes the statement or answers the question.
Find the root if it is a real number.
-$-\sqrt[4]{625}$

Accepted Answer

A)  -4 
B)  -25 
C)  -5 
D)  Not a real number 
A)  -4 
B)  -25 
C)  -5 
D)  Not a real number

Question 6

Express the radical in simplified form.Assume that all variables represent positive real numbers.
-$-\sqrt[4]{80}$

Accepted Answer

A)  $-2 \sqrt[4]{5}$ 
B)  2 
C)  $-5 \sqrt[4]{2}$ 
D)  -2 
A)  $-2 \sqrt[4]{5}$ 
B)  2 
C)  $-5 \sqrt[4]{2}$ 
D)  -2

Question 7

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.
-$\frac{\sqrt[6]{\mathrm{r}^{5}}}{\sqrt[8]{\mathrm{r}^{3}}}$

Accepted Answer

A)  $\sqrt[48]{r^{22}}$ 
B)  $\frac{\sqrt[6]{r^{5}}}{\sqrt[8]{r^{3}}}$ 
C)  $\mathrm{r}$ 
D)  $\sqrt[24]{\mathrm{r}^{11}}$ 
A)  $\sqrt[48]{r^{22}}$ 
B)  $\frac{\sqrt[6]{r^{5}}}{\sqrt[8]{r^{3}}}$ 
C)  $\mathrm{r}$ 
D)  $\sqrt[24]{\mathrm{r}^{11}}$

Question 8

The easiest way to simplify the expression $\frac{4}{6+\sqrt{6}}$ is to multiply both the numerator and denominator by $6+\sqrt{6}$.

Accepted Answer

A) True 
 B)False

Question 9

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

Accepted Answer

A)  $\sqrt[6]{108}$ 
B)  $\sqrt[6]{432}$ 
C)  $\sqrt[6]{144}$ 
D)  $\sqrt[6]{12}$ 
A)  $\sqrt[6]{108}$ 
B)  $\sqrt[6]{432}$ 
C)  $\sqrt[6]{144}$ 
D)  $\sqrt[6]{12}$

Question 10

Provide an appropriate response.
-If $\mathrm{a}<0$, then $\sqrt{-\mathrm{a}}=\mathrm{i} \sqrt{\mathrm{a}}$.

Accepted Answer

A) True 
 B)False

Question 11

Express the radical in simplified form.Assume that all variables represent positive real numbers.
-$-\sqrt{48}$

Accepted Answer

A)  4 
B)  $-16 \sqrt{3}$ 
C)  $-4 \sqrt{3}$ 
D)  6 
A)  4 
B)  $-16 \sqrt{3}$ 
C)  $-4 \sqrt{3}$ 
D)  6

Question 12

Write the expression in lowest terms. Assume that all variables represent positive real numbers.
-$\frac{90+54 \sqrt{21}}{63}$

Accepted Answer

A)  $\frac{30+54 \sqrt{21}}{7}$ 
B)  $\frac{10+6 \sqrt{21}}{7}$ 
C)  $\frac{90+18 \sqrt{7}}{7}$ 
D)  $\frac{30-18 \sqrt{7}}{21}$ 
A)  $\frac{30+54 \sqrt{21}}{7}$ 
B)  $\frac{10+6 \sqrt{21}}{7}$ 
C)  $\frac{90+18 \sqrt{7}}{7}$ 
D)  $\frac{30-18 \sqrt{7}}{21}$

Question 13

Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero.
-$\frac{5 \sqrt{x}}{\sqrt{x}-2 \sqrt{y}}$

Accepted Answer

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

Question 14

Express the radical in simplified form.Assume that all variables represent positive real numbers.
-$\sqrt[3]{\frac{y^{8}}{8}}$

Accepted Answer

A)  $\frac{\mathrm{y}^{2}+\sqrt[3]{\mathrm{y}^{2}}}{2}$ 
B)  $y^{2}-2 \sqrt[3]{y^{2}}$ 
C)  $\frac{\mathrm{y}^{2} \sqrt[3]{\mathrm{y}^{2}}}{2}$ 
D)  $2 y^{2} \sqrt[3]{y^{2}}$ 
A)  $\frac{\mathrm{y}^{2}+\sqrt[3]{\mathrm{y}^{2}}}{2}$ 
B)  $y^{2}-2 \sqrt[3]{y^{2}}$ 
C)  $\frac{\mathrm{y}^{2} \sqrt[3]{\mathrm{y}^{2}}}{2}$ 
D)  $2 y^{2} \sqrt[3]{y^{2}}$

Question 15

Find the distance between the pair of points.
-$(-5,5)$ and $(5,-7)$

Accepted Answer

A)  244 
B)  $2 \sqrt{26}$ 
C)  22 
D)  $2 \sqrt{61}$ 
A)  244 
B)  $2 \sqrt{26}$ 
C)  22 
D)  $2 \sqrt{61}$

Question 16

Simplify the radical. Assume that all variables represent positive real numbers
-$\sqrt[6]{\frac{\mathrm{s}^{3}}{15,625}}$

Accepted Answer

A)  $\sqrt{6 \frac{s^{3}}{15,625}}$ 
B)  $\frac{s}{5}$ 
C)  $\frac{\sqrt[6]{s^{3}}}{5}$ 
D)  $\frac{\sqrt[6]{s}}{5}$ 
A)  $\sqrt{6 \frac{s^{3}}{15,625}}$ 
B)  $\frac{s}{5}$ 
C)  $\frac{\sqrt[6]{s^{3}}}{5}$ 
D)  $\frac{\sqrt[6]{s}}{5}$

Question 17

Find the power of $i$.
-$\mathrm{i}^{8}$

Accepted Answer

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

Question 18

Rewrite the expressions with rational exponents as radical expressions, and then solve the equation.
-$\left(x^{2}-3\right)^{1 / 2}-(x+3)^{1 / 2}=0$

Accepted Answer

A)  $\{-3,3\}$ 
B)  $\{2,3\}$ 
C)  $\{-2,3\}$ 
D)  $\{-3\}$ 
A)  $\{-3,3\}$ 
B)  $\{2,3\}$ 
C)  $\{-2,3\}$ 
D)  $\{-3\}$

Question 19

Rewrite the expressions with rational exponents as radical expressions, and then solve the equation.
-$(x-4)^{1 / 4}+8=0$

Accepted Answer

A)  $\{-1024\}$ 
B)  $\varnothing$ 
C)  $\{1024\}$ 
D)  $\{2\}$ 
A)  $\{-1024\}$ 
B)  $\varnothing$ 
C)  $\{1024\}$ 
D)  $\{2\}$

Question 20

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

Accepted Answer

A)  13 
B)  14 
C)  12 
D)  9 
A)  13 
B)  14 
C)  12 
D)  9

Can the sum be simplified without first simplifying the individual radical expressions? $\sqrt[13]{160}+\sqrt[13]{295,245}$

Explain why $\sqrt[3]{-3}$ and $-\sqrt[3]{3}$ represent the same number.

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt[4]{48}$

$X_{L} is I=\frac{E}{R+\left(X_{L}-X_{C}\right)} . . Use this law to solve the problem. -Find X_{C} if I=6-2 i, E=5-5 i, R=9 , and X_{L}=1 .$ $X_{L}$ is $I=\frac{E}{R+\left(X_{L}-X_{C}\right)}$ . . Use this law to solve the problem. -Find $X_{C}$ if $I=6-2 i, E=5-5 i, R=9$ , and $X_{L}=1$ .

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $-\sqrt[4]{625}$

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $-\sqrt[4]{80}$

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - $\frac{\sqrt[6]{\mathrm{r}^{5}}}{\sqrt[8]{\mathrm{r}^{3}}}$

The easiest way to simplify the expression $\frac{4}{6+\sqrt{6}}$ is to multiply both the numerator and denominator by $6+\sqrt{6}$ .

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

Provide an appropriate response. -If $\mathrm{a}<0$ , then $\sqrt{-\mathrm{a}}=\mathrm{i} \sqrt{\mathrm{a}}$ .

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $-\sqrt{48}$

Write the expression in lowest terms. Assume that all variables represent positive real numbers. - $\frac{90+54 \sqrt{21}}{63}$

Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero. - $\frac{5 \sqrt{x}}{\sqrt{x}-2 \sqrt{y}}$

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt[3]{\frac{y^{8}}{8}}$

Find the distance between the pair of points. - $(-5,5)$ and $(5,-7)$

Simplify the radical. Assume that all variables represent positive real numbers - $\sqrt[6]{\frac{\mathrm{s}^{3}}{15,625}}$

Find the power of $i$ . - $\mathrm{i}^{8}$

Rewrite the expressions with rational exponents as radical expressions, and then solve the equation. - $\left(x^{2}-3\right)^{1 / 2}-(x+3)^{1 / 2}=0$

Rewrite the expressions with rational exponents as radical expressions, and then solve the equation. - $(x-4)^{1 / 4}+8=0$

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

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

Can the sum be simplified without first simplifying the individual radical expressions? 16013+295,24513\sqrt[13]{160}+\sqrt[13]{295,245}13160​+13295,245​

Explain why −33\sqrt[3]{-3}3−3​ and −33-\sqrt[3]{3}−33​ represent the same number.

Express the radical in simplified form.Assume that all variables represent positive real numbers. - 484\sqrt[4]{48}448​

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 XCX_{C}XC​ if I=6−2i,E=5−5i,R=9I=6-2 i, E=5-5 i, R=9I=6−2i,E=5−5i,R=9 , and XL=1X_{L}=1XL​=1 .

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - −6254-\sqrt[4]{625}−4625​

Express the radical in simplified form.Assume that all variables represent positive real numbers. - −804-\sqrt[4]{80}−480​

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - r56r38\frac{\sqrt[6]{\mathrm{r}^{5}}}{\sqrt[8]{\mathrm{r}^{3}}}8r3​6r5​​

The easiest way to simplify the expression 46+6\frac{4}{6+\sqrt{6}}6+6​4​ is to multiply both the numerator and denominator by 6+66+\sqrt{6}6+6​ .

Simplify. Assume that all variables represent positive real numbers. - 3⋅43\sqrt{3} \cdot \sqrt[3]{4}3​⋅34​

Provide an appropriate response. -If a<0\mathrm{a}<0a<0 , then −a=ia\sqrt{-\mathrm{a}}=\mathrm{i} \sqrt{\mathrm{a}}−a​=ia​ .

Express the radical in simplified form.Assume that all variables represent positive real numbers. - −48-\sqrt{48}−48​

Write the expression in lowest terms. Assume that all variables represent positive real numbers. - 90+542163\frac{90+54 \sqrt{21}}{63}6390+5421​​

Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero. - 5xx−2y\frac{5 \sqrt{x}}{\sqrt{x}-2 \sqrt{y}}x​−2y​5x​​

Express the radical in simplified form.Assume that all variables represent positive real numbers. - y883\sqrt[3]{\frac{y^{8}}{8}}38y8​​

Find the distance between the pair of points. - (−5,5)(-5,5)(−5,5) and (5,−7)(5,-7)(5,−7)

Simplify the radical. Assume that all variables represent positive real numbers - s315,6256\sqrt[6]{\frac{\mathrm{s}^{3}}{15,625}}615,625s3​​

Find the power of iii . - i8\mathrm{i}^{8}i8

Rewrite the expressions with rational exponents as radical expressions, and then solve the equation. - (x2−3)1/2−(x+3)1/2=0\left(x^{2}-3\right)^{1 / 2}-(x+3)^{1 / 2}=0(x2−3)1/2−(x+3)1/2=0

Rewrite the expressions with rational exponents as radical expressions, and then solve the equation. - (x−4)1/4+8=0(x-4)^{1 / 4}+8=0(x−4)1/4+8=0

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

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

Can the sum be simplified without first simplifying the individual radical expressions? $\sqrt[13]{160}+\sqrt[13]{295,245}$

Explain why $\sqrt[3]{-3}$ and $-\sqrt[3]{3}$ represent the same number.

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt[4]{48}$

$X_{L} is I=\frac{E}{R+\left(X_{L}-X_{C}\right)} . . Use this law to solve the problem. -Find X_{C} if I=6-2 i, E=5-5 i, R=9 , and X_{L}=1 .$ $X_{L}$ is $I=\frac{E}{R+\left(X_{L}-X_{C}\right)}$ . . Use this law to solve the problem. -Find $X_{C}$ if $I=6-2 i, E=5-5 i, R=9$ , and $X_{L}=1$ .

Choose the one alternative that best completes the statement or answers the question. Find the root if it is a real number. - $-\sqrt[4]{625}$

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $-\sqrt[4]{80}$

Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers. - $\frac{\sqrt[6]{\mathrm{r}^{5}}}{\sqrt[8]{\mathrm{r}^{3}}}$

The easiest way to simplify the expression $\frac{4}{6+\sqrt{6}}$ is to multiply both the numerator and denominator by $6+\sqrt{6}$ .

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

Provide an appropriate response. -If $\mathrm{a}<0$ , then $\sqrt{-\mathrm{a}}=\mathrm{i} \sqrt{\mathrm{a}}$ .

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $-\sqrt{48}$

Write the expression in lowest terms. Assume that all variables represent positive real numbers. - $\frac{90+54 \sqrt{21}}{63}$

Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero. - $\frac{5 \sqrt{x}}{\sqrt{x}-2 \sqrt{y}}$

Express the radical in simplified form.Assume that all variables represent positive real numbers. - $\sqrt[3]{\frac{y^{8}}{8}}$

Find the distance between the pair of points. - $(-5,5)$ and $(5,-7)$

Simplify the radical. Assume that all variables represent positive real numbers - $\sqrt[6]{\frac{\mathrm{s}^{3}}{15,625}}$

Find the power of $i$ . - $\mathrm{i}^{8}$

Rewrite the expressions with rational exponents as radical expressions, and then solve the equation. - $\left(x^{2}-3\right)^{1 / 2}-(x+3)^{1 / 2}=0$

Rewrite the expressions with rational exponents as radical expressions, and then solve the equation. - $(x-4)^{1 / 4}+8=0$