Question 1

$4 \sqrt{19}+7 \sqrt{19}$

Accepted Answer

A)  $11 \sqrt{19}$ 
B)  $-3 \sqrt{19}$ 
C)  $4 \sqrt{19}$ 
D)  $-12 \sqrt{19}$ 
A)  $11 \sqrt{19}$ 
B)  $-3 \sqrt{19}$ 
C)  $4 \sqrt{19}$ 
D)  $-12 \sqrt{19}$

Question 2

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$\sqrt[4]{81 x^{8}}$

Accepted Answer

A)  324 
B)  $3 x^{2}$ 
C)  $-3 x^{2}$ 
D)  $9 x^{2}$ 
A)  324 
B)  $3 x^{2}$ 
C)  $-3 x^{2}$ 
D)  $9 x^{2}$

Question 3

Simplify the expression. Assume all variables represent nonnegative real numbers.
-$\frac{10^{11 / 13}}{10^{-6 / 13}}$

Accepted Answer

A)  $10^{11 / 13}-10^{6 / 13}$ 
B)  $10^{5 / 13}$ 
C)  $10^{17 / 13}$ 
D)  $10^{-66 / 169}$ 
A)  $10^{11 / 13}-10^{6 / 13}$ 
B)  $10^{5 / 13}$ 
C)  $10^{17 / 13}$ 
D)  $10^{-66 / 169}$

Question 4

Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. The easiest way to simplify the expression $\sqrt{\frac{5}{8}}$ is to multiply both the numerator and denominator of $\frac{\sqrt{5}}{\sqrt{8}}$ by $\sqrt{8}$.

Accepted Answer

The statement is false. The easiest way

Question 5

Multiply the conjugates.
-$(3 \sqrt{5}-2 \sqrt{2})(3 \sqrt{5}+2 \sqrt{2})$

Accepted Answer

A)  11 
B)  $53+12 \sqrt{10}$ 
C)  53 
D)  37 
A)  11 
B)  $53+12 \sqrt{10}$ 
C)  53 
D)  37

Question 6

If $a \neq 0, \frac{1}{a}$ is called the reciprocal of a. Use this definition to express the reciprocal of 3 - $4 \mathrm{i}$ in the form a +bi.

Accepted Answer

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

Question 7

How many real square roots does any negative number have?

Accepted Answer

A)  It depends on the number 
B)  None 
C)  One 
D)  Two 
A)  It depends on the number 
B)  None 
C)  One 
D)  Two

Question 8

Add or subtract. Assume all variables represent nonnegative real numbers.

-$\sqrt[3]{27 y}-\sqrt[3]{128 y}$

Accepted Answer

A)  $3 \sqrt[3]{\mathrm{y}}-4 \sqrt[3]{2 \mathrm{y}}$ 
B)  $7 \sqrt[3]{y}$ 
C)  $4 \sqrt[3]{2 y}-3 \sqrt[3]{y}$ 
D)  $3-4 \sqrt[3]{2}$ 
A)  $3 \sqrt[3]{\mathrm{y}}-4 \sqrt[3]{2 \mathrm{y}}$ 
B)  $7 \sqrt[3]{y}$ 
C)  $4 \sqrt[3]{2 y}-3 \sqrt[3]{y}$ 
D)  $3-4 \sqrt[3]{2}$

Question 9

Choose the one alternative that best completes the statement or answers thequestion.
Express in terms of i.
-$\sqrt{-292}$

Accepted Answer

A)  $2 \sqrt{73} i$ 
B)  $-2 \sqrt{73}$ 
C)  $2 \sqrt{73}$ 
D)  $-2 \sqrt{73} i$ 
A)  $2 \sqrt{73} i$ 
B)  $-2 \sqrt{73}$ 
C)  $2 \sqrt{73}$ 
D)  $-2 \sqrt{73} i$

Question 10

Simplify the radical expression. Indicate if the expression is not a real number.
-$\sqrt{-361}$

Accepted Answer

A)  19 
B)  -19 
C)  Not a real number 
D)  180 
A)  19 
B)  -19 
C)  Not a real number 
D)  180

Question 11

Simplify the expression. Assume all variables represent nonnegative real numbers.
-$\frac{\sqrt[10]{\mathrm{x}^{9}}}{\sqrt[12]{\mathrm{x}^{7}}}$

Accepted Answer

A)  $\sqrt[60]{\mathrm{x}^{19}}$ 
B)  $\sqrt[120]{\mathrm{x}^{38}}$ 
C)  $\frac{\sqrt[10]{\mathrm{x}^{9}}}{\sqrt[12]{\mathrm{x}^{7}}}$ 
D)  $\sqrt{\mathrm{x}}$ 
A)  $\sqrt[60]{\mathrm{x}^{19}}$ 
B)  $\sqrt[120]{\mathrm{x}^{38}}$ 
C)  $\frac{\sqrt[10]{\mathrm{x}^{9}}}{\sqrt[12]{\mathrm{x}^{7}}}$ 
D)  $\sqrt{\mathrm{x}}$

Question 12

Simplify. Assume all variables represent nonnegative values.
-$\sqrt{\frac{10}{\mathrm{r}^{4}}}$

Accepted Answer

A)  $\frac{\sqrt{10}}{r^{2}}$ 
B)  $\frac{\sqrt{10}}{\sqrt{\mathrm{r}^{4}}}$ 
C)  $\frac{\sqrt{10 r^{4}}}{r^{4}}$ 
D)  $\frac{\sqrt{10}}{r}$ 
A)  $\frac{\sqrt{10}}{r^{2}}$ 
B)  $\frac{\sqrt{10}}{\sqrt{\mathrm{r}^{4}}}$ 
C)  $\frac{\sqrt{10 r^{4}}}{r^{4}}$ 
D)  $\frac{\sqrt{10}}{r}$

Question 13

Add or subtract. Assume all variables represent nonnegative real numbers.

-$4 \sqrt[3]{8 x}+4 \sqrt[3]{27 x}$

Accepted Answer

A)  $4 \sqrt[3]{35 x}$ 
B)  $20 \sqrt[3]{x}$ 
C)  $5 \sqrt[3]{\mathrm{x}}$ 
D)  $20 \mathrm{x}$ 
A)  $4 \sqrt[3]{35 x}$ 
B)  $20 \sqrt[3]{x}$ 
C)  $5 \sqrt[3]{\mathrm{x}}$ 
D)  $20 \mathrm{x}$

Question 14

If $\mathrm{a}>0$, then $\frac{\mathrm{a}}{\mathrm{i}}=\mathrm{ia}$.

Accepted Answer

A) True 
 B)False

Question 15

$(-5+11 \mathrm{i}) \div(-8 \mathrm{i})$

Accepted Answer

A)  $\frac{11}{8}+\frac{5}{8} \mathrm{i}$ 
B)  $\frac{11}{8}-\frac{5}{8} \mathrm{i}$ 
C)  $-\frac{11}{8}+\frac{5}{8} \mathrm{i}$ 
D)  $-\frac{11}{8}-\frac{5}{8} \mathrm{i}$ 
A)  $\frac{11}{8}+\frac{5}{8} \mathrm{i}$ 
B)  $\frac{11}{8}-\frac{5}{8} \mathrm{i}$ 
C)  $-\frac{11}{8}+\frac{5}{8} \mathrm{i}$ 
D)  $-\frac{11}{8}-\frac{5}{8} \mathrm{i}$

Question 16

Can the sum be simplified without first simplifying the individual radical expressions? $\sqrt[11]{375}+\sqrt[11]{3000}$

Accepted Answer

A) True 
 B)False

Question 17

Find the missing radical expression.
$3 \sqrt{245}-5 \sqrt{847}+(?)=18 \sqrt{5}-30 \sqrt{7}$

Accepted Answer

The answer of Find the missing radical expression.
\(3 \sqrt{245}-5 \sqrt{847}+(?)=18...

Question 18

A ssume all variables represent nonnegative real numbers.
-$\sqrt{2} \cdot \sqrt{4 x^{3}}$

Accepted Answer

A)  $2 \sqrt{2 x^{3}}$ 
B)  $\sqrt{8 x^{3}}$ 
C)  $x \sqrt{8 x}$ 
D)  $2 x \sqrt{2 x}$ 
A)  $2 \sqrt{2 x^{3}}$ 
B)  $\sqrt{8 x^{3}}$ 
C)  $x \sqrt{8 x}$ 
D)  $2 x \sqrt{2 x}$

Question 19

A ssume all variables represent nonnegative real numbers.
-$\sqrt[3]{\mathrm{x}} \cdot \sqrt[3]{\mathrm{x}^{14}}$

Accepted Answer

A)  $x^{4}$ 
B)  $x^{5}$ 
C)  $5 \mathrm{x}$ 
D)  $x^{6}$ 
A)  $x^{4}$ 
B)  $x^{5}$ 
C)  $5 \mathrm{x}$ 
D)  $x^{6}$

Question 20

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

Accepted Answer

A) True 
 B)False

$4 \sqrt{19}+7 \sqrt{19}$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt[4]{81 x^{8}}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\frac{10^{11 / 13}}{10^{-6 / 13}}$

Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. The easiest way to simplify the expression $\sqrt{\frac{5}{8}}$ is to multiply both the numerator and denominator of $\frac{\sqrt{5}}{\sqrt{8}}$ by $\sqrt{8}$ .

Multiply the conjugates. - $(3 \sqrt{5}-2 \sqrt{2})(3 \sqrt{5}+2 \sqrt{2})$

If $a \neq 0, \frac{1}{a}$ is called the reciprocal of a. Use this definition to express the reciprocal of 3 - $4 \mathrm{i}$ in the form a +bi.

How many real square roots does any negative number have?

Add or subtract. Assume all variables represent nonnegative real numbers. - $\sqrt[3]{27 y}-\sqrt[3]{128 y}$

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - $\sqrt{-292}$

Simplify the radical expression. Indicate if the expression is not a real number. - $\sqrt{-361}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\frac{\sqrt[10]{\mathrm{x}^{9}}}{\sqrt[12]{\mathrm{x}^{7}}}$

Simplify. Assume all variables represent nonnegative values. - $\sqrt{\frac{10}{\mathrm{r}^{4}}}$

Add or subtract. Assume all variables represent nonnegative real numbers. - $4 \sqrt[3]{8 x}+4 \sqrt[3]{27 x}$

If $\mathrm{a}>0$ , then $\frac{\mathrm{a}}{\mathrm{i}}=\mathrm{ia}$ .

$(-5+11 \mathrm{i}) \div(-8 \mathrm{i})$

Can the sum be simplified without first simplifying the individual radical expressions? $\sqrt[11]{375}+\sqrt[11]{3000}$

Find the missing radical expression. $3 \sqrt{245}-5 \sqrt{847}+(?)=18 \sqrt{5}-30 \sqrt{7}$

A ssume all variables represent nonnegative real numbers. - $\sqrt{2} \cdot \sqrt{4 x^{3}}$

A ssume all variables represent nonnegative real numbers. - $\sqrt[3]{\mathrm{x}} \cdot \sqrt[3]{\mathrm{x}^{14}}$

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

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 7: Radical Expressions and Equations

419+7194 \sqrt{19}+7 \sqrt{19}419​+719​

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - 81x84\sqrt[4]{81 x^{8}}481x8​

Simplify the expression. Assume all variables represent nonnegative real numbers. - 1011/1310−6/13\frac{10^{11 / 13}}{10^{-6 / 13}}10−6/131011/13​

Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. The easiest way to simplify the expression 58\sqrt{\frac{5}{8}}85​​ is to multiply both the numerator and denominator of 58\frac{\sqrt{5}}{\sqrt{8}}8​5​​ by 8\sqrt{8}8​ .

Multiply the conjugates. - (35−22)(35+22)(3 \sqrt{5}-2 \sqrt{2})(3 \sqrt{5}+2 \sqrt{2})(35​−22​)(35​+22​)

If a≠0,1aa \neq 0, \frac{1}{a}a=0,a1​ is called the reciprocal of a. Use this definition to express the reciprocal of 3 - 4i4 \mathrm{i}4i in the form a +bi.

How many real square roots does any negative number have?

Add or subtract. Assume all variables represent nonnegative real numbers. - 27y3−128y3\sqrt[3]{27 y}-\sqrt[3]{128 y}327y​−3128y​

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - −292\sqrt{-292}−292​

Simplify the radical expression. Indicate if the expression is not a real number. - −361\sqrt{-361}−361​

Simplify the expression. Assume all variables represent nonnegative real numbers. - x910x712\frac{\sqrt[10]{\mathrm{x}^{9}}}{\sqrt[12]{\mathrm{x}^{7}}}12x7​10x9​​

Simplify. Assume all variables represent nonnegative values. - 10r4\sqrt{\frac{10}{\mathrm{r}^{4}}}r410​​

Add or subtract. Assume all variables represent nonnegative real numbers. - 48x3+427x34 \sqrt[3]{8 x}+4 \sqrt[3]{27 x}438x​+4327x​

If a>0\mathrm{a}>0a>0 , then ai=ia\frac{\mathrm{a}}{\mathrm{i}}=\mathrm{ia}ia​=ia .

(−5+11i)÷(−8i)(-5+11 \mathrm{i}) \div(-8 \mathrm{i})(−5+11i)÷(−8i)

Can the sum be simplified without first simplifying the individual radical expressions? 37511+300011\sqrt[11]{375}+\sqrt[11]{3000}11375​+113000​

Find the missing radical expression. 3245−5847+(?)=185−3073 \sqrt{245}-5 \sqrt{847}+(?)=18 \sqrt{5}-30 \sqrt{7}3245​−5847​+(?)=185​−307​

A ssume all variables represent nonnegative real numbers. - 2⋅4x3\sqrt{2} \cdot \sqrt{4 x^{3}}2​⋅4x3​

A ssume all variables represent nonnegative real numbers. - x3⋅x143\sqrt[3]{\mathrm{x}} \cdot \sqrt[3]{\mathrm{x}^{14}}3x​⋅3x14​

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

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

$4 \sqrt{19}+7 \sqrt{19}$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt[4]{81 x^{8}}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\frac{10^{11 / 13}}{10^{-6 / 13}}$

Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. The easiest way to simplify the expression $\sqrt{\frac{5}{8}}$ is to multiply both the numerator and denominator of $\frac{\sqrt{5}}{\sqrt{8}}$ by $\sqrt{8}$ .

Multiply the conjugates. - $(3 \sqrt{5}-2 \sqrt{2})(3 \sqrt{5}+2 \sqrt{2})$

If $a \neq 0, \frac{1}{a}$ is called the reciprocal of a. Use this definition to express the reciprocal of 3 - $4 \mathrm{i}$ in the form a +bi.

Add or subtract. Assume all variables represent nonnegative real numbers. - $\sqrt[3]{27 y}-\sqrt[3]{128 y}$

Choose the one alternative that best completes the statement or answers thequestion. Express in terms of i. - $\sqrt{-292}$

Simplify the radical expression. Indicate if the expression is not a real number. - $\sqrt{-361}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\frac{\sqrt[10]{\mathrm{x}^{9}}}{\sqrt[12]{\mathrm{x}^{7}}}$

Simplify. Assume all variables represent nonnegative values. - $\sqrt{\frac{10}{\mathrm{r}^{4}}}$

Add or subtract. Assume all variables represent nonnegative real numbers. - $4 \sqrt[3]{8 x}+4 \sqrt[3]{27 x}$

If $\mathrm{a}>0$ , then $\frac{\mathrm{a}}{\mathrm{i}}=\mathrm{ia}$ .

$(-5+11 \mathrm{i}) \div(-8 \mathrm{i})$

Can the sum be simplified without first simplifying the individual radical expressions? $\sqrt[11]{375}+\sqrt[11]{3000}$

Find the missing radical expression. $3 \sqrt{245}-5 \sqrt{847}+(?)=18 \sqrt{5}-30 \sqrt{7}$

A ssume all variables represent nonnegative real numbers. - $\sqrt{2} \cdot \sqrt{4 x^{3}}$

A ssume all variables represent nonnegative real numbers. - $\sqrt[3]{\mathrm{x}} \cdot \sqrt[3]{\mathrm{x}^{14}}$

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