Question 1

$-6 \sqrt{12}-7 \sqrt{27}$

Accepted Answer

A)  $9 \sqrt{3}$ 
B)  $-33 \sqrt{3}$ 
C)  $33 \sqrt{3}$ 
D)  $-9 \sqrt{3}$ 
A)  $9 \sqrt{3}$ 
B)  $-33 \sqrt{3}$ 
C)  $33 \sqrt{3}$ 
D)  $-9 \sqrt{3}$

Question 2

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$\sqrt{\mathrm{t}^{7}}$

Accepted Answer

A)  $t^{4} \sqrt{t}$ 
B)  $t^{14} \sqrt{t}$ 
C)  $t^{3} \sqrt{t}$ 
D)  $\mathrm{t}^{7} \sqrt{\mathrm{t}}$ 
A)  $t^{4} \sqrt{t}$ 
B)  $t^{14} \sqrt{t}$ 
C)  $t^{3} \sqrt{t}$ 
D)  $\mathrm{t}^{7} \sqrt{\mathrm{t}}$

Question 3

$\sqrt{125}$

Accepted Answer

A)  11 
B)  5 
C)  $5 \sqrt{5}$ 
D)  $25 \sqrt{5}$ 
A)  11 
B)  5 
C)  $5 \sqrt{5}$ 
D)  $25 \sqrt{5}$

Question 4

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$\sqrt[3]{27 \mathrm{x}^{4} \mathrm{y}^{5}}$

Accepted Answer

A)  $3 x y \sqrt[3]{x^{2} y}$ 
B)  $3 x y \sqrt[3]{x y}$ 
C)  $x y \sqrt[3]{x y^{2}}$ 
D)  $3 x y \sqrt[3]{x y^{2}}$ 
A)  $3 x y \sqrt[3]{x^{2} y}$ 
B)  $3 x y \sqrt[3]{x y}$ 
C)  $x y \sqrt[3]{x y^{2}}$ 
D)  $3 x y \sqrt[3]{x y^{2}}$

Question 5

Find the domain of the function. Express the answer in interval notation.
-$f(x)=\sqrt[5]{2 x-4}$

Accepted Answer

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

Question 6

Simplify. Assume all variables represent nonnegative values.
-$\sqrt{\frac{7}{9}}$

Accepted Answer

A)  $3 \sqrt{7}$ 
B)  $9 \sqrt{7}$ 
C)  $\frac{\sqrt{7}}{3}$ 
D)  $\frac{\sqrt{7}}{\sqrt{9}}$ 
A)  $3 \sqrt{7}$ 
B)  $9 \sqrt{7}$ 
C)  $\frac{\sqrt{7}}{3}$ 
D)  $\frac{\sqrt{7}}{\sqrt{9}}$

Question 7

Multiply.
-$\sqrt{-100} \cdot \sqrt{-81}$

Accepted Answer

A)  $90 \mathrm{i}$ 
B)  90 
C)  -90 
D)  $-90 \mathrm{i}$ 
A)  $90 \mathrm{i}$ 
B)  90 
C)  -90 
D)  $-90 \mathrm{i}$

Question 8

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers.
-$\sqrt{\frac{245 \mathrm{x}^{3}}{\mathrm{y} 5}}$

Accepted Answer

A)  $\frac{7 x}{y 2} \sqrt{\frac{5 x}{y}}$ 
B)  $\frac{x \sqrt{245 x y}}{y 3}$ 
C)  $\frac{7 x^{3} \sqrt{5}}{y 5}$ 
D)  $\frac{7 x \sqrt{5 x y}}{y 3}$ 
A)  $\frac{7 x}{y 2} \sqrt{\frac{5 x}{y}}$ 
B)  $\frac{x \sqrt{245 x y}}{y 3}$ 
C)  $\frac{7 x^{3} \sqrt{5}}{y 5}$ 
D)  $\frac{7 x \sqrt{5 x y}}{y 3}$

Question 9

Multiply the conjugates.
-$(3+2 i)(3-2 i)$

Accepted Answer

A)  5 
B)  $9-4 \mathrm{i}$ 
C)  $9+4 \mathrm{i}$ 
D)  13 
A)  5 
B)  $9-4 \mathrm{i}$ 
C)  $9+4 \mathrm{i}$ 
D)  13

Question 10

Simplify the radical expression. If appropriate, include absolute values.
-$\sqrt{25 x^{2}+40 x+16}$

Accepted Answer

A)  $|5 x+4|$ 
B)  $|5 x|+4$ 
C)  $5 x+4$ 
D)  $5 x+\sqrt{20 x}$ 
A)  $|5 x+4|$ 
B)  $|5 x|+4$ 
C)  $5 x+4$ 
D)  $5 x+\sqrt{20 x}$

Question 11

$3 \sqrt{2}+5 \sqrt{2}$

Accepted Answer

A)  16 
B)  $8 \sqrt{4}$ 
C)  $15 \sqrt{2}$ 
D)  $8 \sqrt{2}$ 
A)  16 
B)  $8 \sqrt{4}$ 
C)  $15 \sqrt{2}$ 
D)  $8 \sqrt{2}$

Question 12

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers.
-$\sqrt{\frac{9}{20}}$

Accepted Answer

A)  $\frac{3 \sqrt{5}}{5}$ 
B)  $3 \sqrt{5}$ 
C)  $\frac{3 \sqrt{5}}{10}$ 
D)  20 
A)  $\frac{3 \sqrt{5}}{5}$ 
B)  $3 \sqrt{5}$ 
C)  $\frac{3 \sqrt{5}}{10}$ 
D)  20

Question 13

Factor completely
-$x^{9 / 8}-17 x^{1 / 8}+16 x^{-7 / 8}$

Accepted Answer

A)  $x^{-7 / 8}\left(x^{2}+x-16\right)$ 
B)  $x^{-7 / 8}\left(x^{2}-x+16\right)$ 
C)  $x^{-7 / 8}(x+1)(x-16)$ 
D)  $x^{-7 / 8}(x-1)(x-16)$ 
A)  $x^{-7 / 8}\left(x^{2}+x-16\right)$ 
B)  $x^{-7 / 8}\left(x^{2}-x+16\right)$ 
C)  $x^{-7 / 8}(x+1)(x-16)$ 
D)  $x^{-7 / 8}(x-1)(x-16)$

Question 14

Explain why the sum $\sqrt[4]{81}-\sqrt[4]{625}-\sqrt[3]{216}$ can be simplified quickly.

Accepted Answer

Each radic

Question 15

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers.
-$\left(169 r^{14}\right)^{1 / 2}$

Accepted Answer

A)  $\sqrt{169 r^{14}}$ 
B)  $13 r^{7}$ 
C)  $13 \sqrt{r^{14}}$ 
D)  $13 r^{14}$ 
A)  $\sqrt{169 r^{14}}$ 
B)  $13 r^{7}$ 
C)  $13 \sqrt{r^{14}}$ 
D)  $13 r^{14}$

Question 16

Find the domain of the function. Express the answer in interval notation.
-$f(x)=5+2 \sqrt[6]{3 t-42}$

Accepted Answer

A)  $[14, \infty)$ 
B)  $(-\infty, 14)$ 
C)  $(-\infty, \infty)$ 
D)  $[-14, \infty)$ 
A)  $[14, \infty)$ 
B)  $(-\infty, 14)$ 
C)  $(-\infty, \infty)$ 
D)  $[-14, \infty)$

Question 17

$-6 \mathrm{i} \div(-10+2 \mathrm{i})$

Accepted Answer

A)  $-\frac{3}{26}+\frac{15}{26} \mathrm{i}$ 
B)  $\frac{1}{8}+\frac{5}{8} \mathrm{i}$ 
C)  $-\frac{1}{8}+\frac{5}{8} \mathrm{i}$ 
D)  $\frac{3}{26}+\frac{15}{26} \mathrm{i}$ 
A)  $-\frac{3}{26}+\frac{15}{26} \mathrm{i}$ 
B)  $\frac{1}{8}+\frac{5}{8} \mathrm{i}$ 
C)  $-\frac{1}{8}+\frac{5}{8} \mathrm{i}$ 
D)  $\frac{3}{26}+\frac{15}{26} \mathrm{i}$

Question 18

Simplify the radical expression. Indicate if the expression is not a real number.
-$\sqrt{-\frac{361}{36}}$

Accepted Answer

A)  $\frac{19}{6}$ 
B)  Not a real number 
C)  - 10 
D)  $-\frac{19}{6}$ 
A)  $\frac{19}{6}$ 
B)  Not a real number 
C)  - 10 
D)  $-\frac{19}{6}$

Question 19

Find the missing number
-$\sqrt{?}=17$

Accepted Answer

A)  19 
B)  34 
C)  578 
D)  289 
A)  19 
B)  34 
C)  578 
D)  289

Question 20

What is the smallest power to which you can raise both sides of the radical equation
$\sqrt[n]{7 \mathrm{x}+1}=\sqrt[m]{-9-8 \mathrm{x}}$ so that the radicals are eliminated. Assume that $\mathrm{m}$ and $\mathrm{n}$ are relatively prime.

Accepted Answer

A)  $\mathrm{mn}$ 
B)  $\frac{m+n}{m n}$ 
C)  $\frac{1}{m}+\frac{1}{n}$ 
D)  $m+n$ 
A)  $\mathrm{mn}$ 
B)  $\frac{m+n}{m n}$ 
C)  $\frac{1}{m}+\frac{1}{n}$ 
D)  $m+n$

$-6 \sqrt{12}-7 \sqrt{27}$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt{\mathrm{t}^{7}}$

$\sqrt{125}$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt[3]{27 \mathrm{x}^{4} \mathrm{y}^{5}}$

Find the domain of the function. Express the answer in interval notation. - $f(x)=\sqrt[5]{2 x-4}$

Simplify. Assume all variables represent nonnegative values. - $\sqrt{\frac{7}{9}}$

Multiply. - $\sqrt{-100} \cdot \sqrt{-81}$

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - $\sqrt{\frac{245 \mathrm{x}^{3}}{\mathrm{y} 5}}$

Multiply the conjugates. - $(3+2 i)(3-2 i)$

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt{25 x^{2}+40 x+16}$

$3 \sqrt{2}+5 \sqrt{2}$

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - $\sqrt{\frac{9}{20}}$

Factor completely - $x^{9 / 8}-17 x^{1 / 8}+16 x^{-7 / 8}$

Explain why the sum $\sqrt[4]{81}-\sqrt[4]{625}-\sqrt[3]{216}$ can be simplified quickly.

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $\left(169 r^{14}\right)^{1 / 2}$

Find the domain of the function. Express the answer in interval notation. - $f(x)=5+2 \sqrt[6]{3 t-42}$

$-6 \mathrm{i} \div(-10+2 \mathrm{i})$

Simplify the radical expression. Indicate if the expression is not a real number. - $\sqrt{-\frac{361}{36}}$

Find the missing number - $\sqrt{?}=17$

What is the smallest power to which you can raise both sides of the radical equation $\sqrt[n]{7 \mathrm{x}+1}=\sqrt[m]{-9-8 \mathrm{x}}$ so that the radicals are eliminated. Assume that $\mathrm{m}$ and $\mathrm{n}$ are relatively prime.

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

−612−727-6 \sqrt{12}-7 \sqrt{27}−612​−727​

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - t7\sqrt{\mathrm{t}^{7}}t7​

125\sqrt{125}125​

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - 27x4y53\sqrt[3]{27 \mathrm{x}^{4} \mathrm{y}^{5}}327x4y5​

Find the domain of the function. Express the answer in interval notation. - f(x)=2x−45f(x)=\sqrt[5]{2 x-4}f(x)=52x−4​

Simplify. Assume all variables represent nonnegative values. - 79\sqrt{\frac{7}{9}}97​​

Multiply. - −100⋅−81\sqrt{-100} \cdot \sqrt{-81}−100​⋅−81​

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - 245x3y5\sqrt{\frac{245 \mathrm{x}^{3}}{\mathrm{y} 5}}y5245x3​​

Multiply the conjugates. - (3+2i)(3−2i)(3+2 i)(3-2 i)(3+2i)(3−2i)

Simplify the radical expression. If appropriate, include absolute values. - 25x2+40x+16\sqrt{25 x^{2}+40 x+16}25x2+40x+16​

32+523 \sqrt{2}+5 \sqrt{2}32​+52​

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - 920\sqrt{\frac{9}{20}}209​​

Factor completely - x9/8−17x1/8+16x−7/8x^{9 / 8}-17 x^{1 / 8}+16 x^{-7 / 8}x9/8−17x1/8+16x−7/8

Explain why the sum 814−6254−2163\sqrt[4]{81}-\sqrt[4]{625}-\sqrt[3]{216}481​−4625​−3216​ can be simplified quickly.

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - (169r14)1/2\left(169 r^{14}\right)^{1 / 2}(169r14)1/2

Find the domain of the function. Express the answer in interval notation. - f(x)=5+23t−426f(x)=5+2 \sqrt[6]{3 t-42}f(x)=5+263t−42​

−6i÷(−10+2i)-6 \mathrm{i} \div(-10+2 \mathrm{i})−6i÷(−10+2i)

Simplify the radical expression. Indicate if the expression is not a real number. - −36136\sqrt{-\frac{361}{36}}−36361​​

Find the missing number - ?=17\sqrt{?}=17?​=17

What is the smallest power to which you can raise both sides of the radical equation 7x+1n=−9−8xm\sqrt[n]{7 \mathrm{x}+1}=\sqrt[m]{-9-8 \mathrm{x}}n7x+1​=m−9−8x​ so that the radicals are eliminated. Assume that m\mathrm{m}m and n\mathrm{n}n are relatively prime.

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

$-6 \sqrt{12}-7 \sqrt{27}$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt{\mathrm{t}^{7}}$

$\sqrt{125}$

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt[3]{27 \mathrm{x}^{4} \mathrm{y}^{5}}$

Find the domain of the function. Express the answer in interval notation. - $f(x)=\sqrt[5]{2 x-4}$

Simplify. Assume all variables represent nonnegative values. - $\sqrt{\frac{7}{9}}$

Multiply. - $\sqrt{-100} \cdot \sqrt{-81}$

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - $\sqrt{\frac{245 \mathrm{x}^{3}}{\mathrm{y} 5}}$

Multiply the conjugates. - $(3+2 i)(3-2 i)$

Simplify the radical expression. If appropriate, include absolute values. - $\sqrt{25 x^{2}+40 x+16}$

$3 \sqrt{2}+5 \sqrt{2}$

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - $\sqrt{\frac{9}{20}}$

Factor completely - $x^{9 / 8}-17 x^{1 / 8}+16 x^{-7 / 8}$

Explain why the sum $\sqrt[4]{81}-\sqrt[4]{625}-\sqrt[3]{216}$ can be simplified quickly.

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $\left(169 r^{14}\right)^{1 / 2}$

Find the domain of the function. Express the answer in interval notation. - $f(x)=5+2 \sqrt[6]{3 t-42}$

$-6 \mathrm{i} \div(-10+2 \mathrm{i})$

Simplify the radical expression. Indicate if the expression is not a real number. - $\sqrt{-\frac{361}{36}}$

Find the missing number - $\sqrt{?}=17$

What is the smallest power to which you can raise both sides of the radical equation $\sqrt[n]{7 \mathrm{x}+1}=\sqrt[m]{-9-8 \mathrm{x}}$ so that the radicals are eliminated. Assume that $\mathrm{m}$ and $\mathrm{n}$ are relatively prime.