Question 1

Simplify the expression. Assume all variables represent nonnegative real numbers.
-$\sqrt[5]{\mathrm{t}} \cdot \sqrt[4]{\mathrm{t}^{3}}$

Accepted Answer

A)  $\sqrt[9]{t^{3}}$ 
B)  $\sqrt[20]{t^{4}}$ 
C)  $\sqrt[20]{\mathrm{t}^{19}}$ 
D)  $\sqrt[9]{t^{4}}$ 
A)  $\sqrt[9]{t^{3}}$ 
B)  $\sqrt[20]{t^{4}}$ 
C)  $\sqrt[20]{\mathrm{t}^{19}}$ 
D)  $\sqrt[9]{t^{4}}$

Question 2

Solve. Check for extraneous solutions.
-$(x-5)^{1 / 2}=-3$

Accepted Answer

A)  $\{14\}$ 
B)  $\{4\}$ 
C)  $\{2\}$ 
D)  $\varnothing$ 
A)  $\{14\}$ 
B)  $\{4\}$ 
C)  $\{2\}$ 
D)  $\varnothing$

Question 3

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers.
-$125^{4 / 3}$

Accepted Answer

A)  15,625 
B)  3125 
C)  78,125 
D)  625 
A)  15,625 
B)  3125 
C)  78,125 
D)  625

Question 4

Simplify by rationalizing the denominator. Write your answer in a + bi form.
-$\frac{5+4 i}{8-7 i}$

Accepted Answer

A)  $\frac{4}{5}$ 
B)  $\frac{68}{15}-\frac{67}{15} \mathrm{i}$ 
C)  $\frac{12}{113}+\frac{67}{113} \mathrm{i}$ 
D)  $\frac{68}{113}+\frac{3}{113} \mathrm{i}$ 
A)  $\frac{4}{5}$ 
B)  $\frac{68}{15}-\frac{67}{15} \mathrm{i}$ 
C)  $\frac{12}{113}+\frac{67}{113} \mathrm{i}$ 
D)  $\frac{68}{113}+\frac{3}{113} \mathrm{i}$

Question 5

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$\sqrt[6]{\mathrm{x}^{6} \mathrm{y}^{1 \mathrm{z}^{5}}}$

Accepted Answer

A)  $x \sqrt[6]{y^{5} z^{5}}$ 
B)  $x y \sqrt[6]{y^{5} z^{5}}$ 
C)  $x y z \sqrt[6]{y^{5} z^{5}}$ 
D)  $x y \sqrt{y^{5} z^{5}}$ 
A)  $x \sqrt[6]{y^{5} z^{5}}$ 
B)  $x y \sqrt[6]{y^{5} z^{5}}$ 
C)  $x y z \sqrt[6]{y^{5} z^{5}}$ 
D)  $x y \sqrt{y^{5} z^{5}}$

Question 6

Find the missing complex number
-$(-4+\mathrm{i})+?=8+9 \mathrm{i}$

Accepted Answer

A)  $12+8 \mathrm{i}$ 
B)  $-12-8 i$ 
C)  $12-8 \mathrm{i}$ 
D)  $4+10 \mathrm{i}$ 
A)  $12+8 \mathrm{i}$ 
B)  $-12-8 i$ 
C)  $12-8 \mathrm{i}$ 
D)  $4+10 \mathrm{i}$

Question 7

Find the missing radical expression.
$$(6 \sqrt[3]{4}-9 \sqrt{6})+(?)=15 \sqrt[3]{4}-5 \sqrt{6}$$

Accepted Answer

The answer of Find the missing radical expression.
\[(6 \sqrt[3]{4}-9 \sqrt{6})+(?)=15...

Question 8

Solve. Check for extraneous solutions.
-$\sqrt{3 \mathrm{x}-2}+\sqrt{11+\mathrm{x}}=-1$

Accepted Answer

A)  $\{5\}$ 
B)  $\left\{-\frac{5}{2}\right\}$ 
C)  $\{0\}$ 
D)  $\varnothing$ 
A)  $\{5\}$ 
B)  $\left\{-\frac{5}{2}\right\}$ 
C)  $\{0\}$ 
D)  $\varnothing$

Question 9

Simplify. Assume all variables represent nonnegative values.
-$\sqrt{\frac{63 \mathrm{a}^{2} \mathrm{~b}}{\mathrm{c}^{2}}}$

Accepted Answer

A)  $\frac{3 \sqrt{7 a^{2} b}}{c}$ 
B)  $\frac{9 a \sqrt{7 b}}{c}$ 
C)  $\frac{a \sqrt{63 b}}{c}$ 
D)  $\frac{3 a \sqrt{7 b}}{c}$ 
A)  $\frac{3 \sqrt{7 a^{2} b}}{c}$ 
B)  $\frac{9 a \sqrt{7 b}}{c}$ 
C)  $\frac{a \sqrt{63 b}}{c}$ 
D)  $\frac{3 a \sqrt{7 b}}{c}$

Question 10

A ssume all variables represent nonnegative real numbers.
-$\sqrt{2} \cdot \sqrt{50}$

Accepted Answer

A)  100 
B)  20 
C)  200 
D)  10 
A)  100 
B)  20 
C)  200 
D)  10

Question 11

Solve. Check for extraneous solutions.
-$\sqrt{x^{2}-3 x+18}=x+2$

Accepted Answer

A)  $\{4\}$ 
B)  $\{2\}$. 
C)  $\{0\}$ 
D)  $\{-2\}$ 
A)  $\{4\}$ 
B)  $\{2\}$. 
C)  $\{0\}$ 
D)  $\{-2\}$

Question 12

Use the Babylonian method to approximate the given square root to the nearest thousandth.
-$\sqrt{47}$

Accepted Answer

A)  6.928 
B)  6.782 
C)  6.856 
D)  7.071 
A)  6.928 
B)  6.782 
C)  6.856 
D)  7.071

Question 13

Find the domain of the function. Express the answer in interval notation.
-$f(x)=\sqrt{x+13}$

Accepted Answer

A)  $(-\infty, 13)$ 
B)  $[13, \infty)$ 
C)  $(-\infty,-13)$ 
D)  $[-13, \infty)$ 
A)  $(-\infty, 13)$ 
B)  $[13, \infty)$ 
C)  $(-\infty,-13)$ 
D)  $[-13, \infty)$

Question 14

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers.
-$400^{1 / 2}$

Accepted Answer

A)  80 
B)  40 
C)  10 
D)  20 
A)  80 
B)  40 
C)  10 
D)  20

Question 15

Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. Assume that $\mathrm{x}$ represents a positive real number. $\sqrt{\mathrm{x}} \cdot \sqrt{\mathrm{x}}=\mathrm{x}$

Accepted Answer

A) True 
 B)False

Question 16

Explain why if $\mathrm{n}$ is odd, $\mathrm{x}^{1 / \mathrm{n}}$ is defined even if $\mathrm{x}$ is negative.

Accepted Answer

Answers many vary. One possibi

Question 17

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 $\sqrt[3]{\frac{5}{49}}$ is to multiply both the numerator and denominator of $\frac{\sqrt[3]{5}}{\sqrt[3]{49}}$ by $\sqrt[3]{49}$

Accepted Answer

The statement is false. The easiest way

Question 18

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

Accepted Answer

A)  9 
B)  $5-2 \sqrt{2}$ 
C)  3 
D)  1 
A)  9 
B)  $5-2 \sqrt{2}$ 
C)  3 
D)  1

Question 19

Find the domain of the function. Express the answer in interval notation.
-$g(x)=\sqrt{5 x^{2}+10}$

Accepted Answer

A)  $(-2, \infty)$ 
B)  $(-\infty, \infty)$ 
C)  $[-2, \infty)$ 
D)  $[0, \infty)$ 
A)  $(-2, \infty)$ 
B)  $(-\infty, \infty)$ 
C)  $[-2, \infty)$ 
D)  $[0, \infty)$

Question 20

Solve. Check for extraneous solutions.
-$\sqrt{\mathrm{x}+6}+\sqrt{2-\mathrm{x}}=4$

Accepted Answer

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

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\sqrt[5]{\mathrm{t}} \cdot \sqrt[4]{\mathrm{t}^{3}}$

Solve. Check for extraneous solutions. - $(x-5)^{1 / 2}=-3$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $125^{4 / 3}$

Simplify by rationalizing the denominator. Write your answer in a + bi form. - $\frac{5+4 i}{8-7 i}$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt[6]{\mathrm{x}^{6} \mathrm{y}^{1 \mathrm{z}^{5}}}$

Find the missing complex number - $(-4+\mathrm{i})+?=8+9 \mathrm{i}$

Find the missing radical expression. $(6 \sqrt[3]{4}-9 \sqrt{6})+(?)=15 \sqrt[3]{4}-5 \sqrt{6}$

Solve. Check for extraneous solutions. - $\sqrt{3 \mathrm{x}-2}+\sqrt{11+\mathrm{x}}=-1$

Simplify. Assume all variables represent nonnegative values. - $\sqrt{\frac{63 \mathrm{a}^{2} \mathrm{~b}}{\mathrm{c}^{2}}}$

A ssume all variables represent nonnegative real numbers. - $\sqrt{2} \cdot \sqrt{50}$

Solve. Check for extraneous solutions. - $\sqrt{x^{2}-3 x+18}=x+2$

Use the Babylonian method to approximate the given square root to the nearest thousandth. - $\sqrt{47}$

Find the domain of the function. Express the answer in interval notation. - $f(x)=\sqrt{x+13}$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $400^{1 / 2}$

Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. Assume that $\mathrm{x}$ represents a positive real number. $\sqrt{\mathrm{x}} \cdot \sqrt{\mathrm{x}}=\mathrm{x}$

Explain why if $\mathrm{n}$ is odd, $\mathrm{x}^{1 / \mathrm{n}}$ is defined even if $\mathrm{x}$ is negative.

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 $\sqrt[3]{\frac{5}{49}}$ is to multiply both the numerator and denominator of $\frac{\sqrt[3]{5}}{\sqrt[3]{49}}$ by $\sqrt[3]{49}$

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

Find the domain of the function. Express the answer in interval notation. - $g(x)=\sqrt{5 x^{2}+10}$

Solve. Check for extraneous solutions. - $\sqrt{\mathrm{x}+6}+\sqrt{2-\mathrm{x}}=4$

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

Simplify the expression. Assume all variables represent nonnegative real numbers. - t5⋅t34\sqrt[5]{\mathrm{t}} \cdot \sqrt[4]{\mathrm{t}^{3}}5t​⋅4t3​

Solve. Check for extraneous solutions. - (x−5)1/2=−3(x-5)^{1 / 2}=-3(x−5)1/2=−3

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - 1254/3125^{4 / 3}1254/3

Simplify by rationalizing the denominator. Write your answer in a + bi form. - 5+4i8−7i\frac{5+4 i}{8-7 i}8−7i5+4i​

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - x6y1z56\sqrt[6]{\mathrm{x}^{6} \mathrm{y}^{1 \mathrm{z}^{5}}}6x6y1z5​

Find the missing complex number - (−4+i)+?=8+9i(-4+\mathrm{i})+?=8+9 \mathrm{i}(−4+i)+?=8+9i

Find the missing radical expression. (643−96)+(?)=1543−56(6 \sqrt[3]{4}-9 \sqrt{6})+(?)=15 \sqrt[3]{4}-5 \sqrt{6}(634​−96​)+(?)=1534​−56​

Solve. Check for extraneous solutions. - 3x−2+11+x=−1\sqrt{3 \mathrm{x}-2}+\sqrt{11+\mathrm{x}}=-13x−2​+11+x​=−1

Simplify. Assume all variables represent nonnegative values. - 63a2 bc2\sqrt{\frac{63 \mathrm{a}^{2} \mathrm{~b}}{\mathrm{c}^{2}}}c263a2 b​​

A ssume all variables represent nonnegative real numbers. - 2⋅50\sqrt{2} \cdot \sqrt{50}2​⋅50​

Solve. Check for extraneous solutions. - x2−3x+18=x+2\sqrt{x^{2}-3 x+18}=x+2x2−3x+18​=x+2

Use the Babylonian method to approximate the given square root to the nearest thousandth. - 47\sqrt{47}47​

Find the domain of the function. Express the answer in interval notation. - f(x)=x+13f(x)=\sqrt{x+13}f(x)=x+13​

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - 4001/2400^{1 / 2}4001/2

Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. Assume that x\mathrm{x}x represents a positive real number. x⋅x=x\sqrt{\mathrm{x}} \cdot \sqrt{\mathrm{x}}=\mathrm{x}x​⋅x​=x

Explain why if n\mathrm{n}n is odd, x1/n\mathrm{x}^{1 / \mathrm{n}}x1/n is defined even if x\mathrm{x}x is negative.

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

Find the domain of the function. Express the answer in interval notation. - g(x)=5x2+10g(x)=\sqrt{5 x^{2}+10}g(x)=5x2+10​

Solve. Check for extraneous solutions. - x+6+2−x=4\sqrt{\mathrm{x}+6}+\sqrt{2-\mathrm{x}}=4x+6​+2−x​=4

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

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\sqrt[5]{\mathrm{t}} \cdot \sqrt[4]{\mathrm{t}^{3}}$

Solve. Check for extraneous solutions. - $(x-5)^{1 / 2}=-3$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $125^{4 / 3}$

Simplify by rationalizing the denominator. Write your answer in a + bi form. - $\frac{5+4 i}{8-7 i}$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt[6]{\mathrm{x}^{6} \mathrm{y}^{1 \mathrm{z}^{5}}}$

Find the missing complex number - $(-4+\mathrm{i})+?=8+9 \mathrm{i}$

Find the missing radical expression. $(6 \sqrt[3]{4}-9 \sqrt{6})+(?)=15 \sqrt[3]{4}-5 \sqrt{6}$

Solve. Check for extraneous solutions. - $\sqrt{3 \mathrm{x}-2}+\sqrt{11+\mathrm{x}}=-1$

Simplify. Assume all variables represent nonnegative values. - $\sqrt{\frac{63 \mathrm{a}^{2} \mathrm{~b}}{\mathrm{c}^{2}}}$

A ssume all variables represent nonnegative real numbers. - $\sqrt{2} \cdot \sqrt{50}$

Solve. Check for extraneous solutions. - $\sqrt{x^{2}-3 x+18}=x+2$

Use the Babylonian method to approximate the given square root to the nearest thousandth. - $\sqrt{47}$

Find the domain of the function. Express the answer in interval notation. - $f(x)=\sqrt{x+13}$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $400^{1 / 2}$

Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. Assume that $\mathrm{x}$ represents a positive real number. $\sqrt{\mathrm{x}} \cdot \sqrt{\mathrm{x}}=\mathrm{x}$

Explain why if $\mathrm{n}$ is odd, $\mathrm{x}^{1 / \mathrm{n}}$ is defined even if $\mathrm{x}$ is negative.

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

Find the domain of the function. Express the answer in interval notation. - $g(x)=\sqrt{5 x^{2}+10}$

Solve. Check for extraneous solutions. - $\sqrt{\mathrm{x}+6}+\sqrt{2-\mathrm{x}}=4$