Question 1

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers.
-$\sqrt{\frac{81}{10}}$

Accepted Answer

A)  $\frac{9 \sqrt{10}}{10}$ 
B)  $\frac{81 \sqrt{10}}{10}$ 
C)  $9 \sqrt{10}$ 
D)  109 
A)  $\frac{9 \sqrt{10}}{10}$ 
B)  $\frac{81 \sqrt{10}}{10}$ 
C)  $9 \sqrt{10}$ 
D)  109

Question 2

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers.
-$625^{5 / 4}$

Accepted Answer

A)  $1,953,125$ 
B)  3125 
C)  78,125 
D)  390,625 
A)  $1,953,125$ 
B)  3125 
C)  78,125 
D)  390,625

Question 3

Simplify the expression. Assume all variables represent nonnegative real numbers.
-$x^{1 / 7} \cdot x^{6 / 7}$

Accepted Answer

A)  $\mathrm{x}$ 
B)  $x^{6 / 49}$ 
C)  $x^{6 / 7}$ 
D)  $\frac{1}{x}$ 
A)  $\mathrm{x}$ 
B)  $x^{6 / 49}$ 
C)  $x^{6 / 7}$ 
D)  $\frac{1}{x}$

Question 4

olve. Check for extraneous solutions.
-$\sqrt[4]{2 \mathrm{x}-2}+7=19$

Accepted Answer

A)  $\{25\}$ 
B)  $\{20,738\}$ 
C)  $\{-887\}$ 
D)  $\{10,369\}$ 
A)  $\{25\}$ 
B)  $\{20,738\}$ 
C)  $\{-887\}$ 
D)  $\{10,369\}$

Question 5

$\mathrm{i}^{3}=-\mathrm{i}$

Accepted Answer

A) True 
 B)False

Question 6

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

Accepted Answer

A)  $\{3\}$ 
B)  $\{-3,-1\}$ 
C)  $\{3,-1\}$. 
D)  $\varnothing$ 
A)  $\{3\}$ 
B)  $\{-3,-1\}$ 
C)  $\{3,-1\}$. 
D)  $\varnothing$

Question 7

Rationalize the denominator and simplify.
-$\frac{\sqrt{5}}{5 \sqrt{3}-\sqrt{5}}$

Accepted Answer

A)  $\frac{1}{14}(\sqrt{15}-1)$ 
B)  $\frac{1}{16}(\sqrt{15}+1)$ 
C)  $\frac{1}{14}(\sqrt{3}+1)$ 
D)  $\frac{1}{14}(\sqrt{15}+1)$ 
A)  $\frac{1}{14}(\sqrt{15}-1)$ 
B)  $\frac{1}{16}(\sqrt{15}+1)$ 
C)  $\frac{1}{14}(\sqrt{3}+1)$ 
D)  $\frac{1}{14}(\sqrt{15}+1)$

Question 8

Simplify by rationalizing the denominator. Write your answer in a + bi form.
-$\frac{4+3 i}{5+2 i}$

Accepted Answer

A)  $\frac{26}{29}+\frac{7}{29} \mathrm{i}$ 
B)  $\frac{2}{3}-\frac{1}{3} \mathrm{i}$ 
C)  $\frac{14}{29}-\frac{23}{29} \mathrm{i}$ 
D)  $\frac{26}{21}-\frac{1}{3} \mathrm{i}$ 
A)  $\frac{26}{29}+\frac{7}{29} \mathrm{i}$ 
B)  $\frac{2}{3}-\frac{1}{3} \mathrm{i}$ 
C)  $\frac{14}{29}-\frac{23}{29} \mathrm{i}$ 
D)  $\frac{26}{21}-\frac{1}{3} \mathrm{i}$

Question 9

Find the sum graphically
-$(2+4 i)+(3+2 i)$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 10

If $a>0$ and $b>0$, then $\sqrt{-a} \cdot \sqrt{b}=i \sqrt{a b}$.

Accepted Answer

A) True 
 B)False

Question 11

Multiply
-$(7+\sqrt{3})^{2}$

Accepted Answer

A)  $49+14 \sqrt{3}$ 
B)  $52+14 \sqrt{3}$ 
C)  $52+7 \sqrt{3}$ 
D)  $10+14 \sqrt{3}$ 
A)  $49+14 \sqrt{3}$ 
B)  $52+14 \sqrt{3}$ 
C)  $52+7 \sqrt{3}$ 
D)  $10+14 \sqrt{3}$

Question 12

$\mathrm{i}^{7}$

Accepted Answer

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

Question 13

The radius of a sphere depends on its surface area, $S$, and is given by the formula $r=\sqrt{\frac{\mathrm{S}}{4 \pi}}$
What is the surface area of a sphere with radius of 7.1 inches? Use 3.14 for $\pi$. Round to the nearest tenth of a square inch.

Accepted Answer

A)  89.2 square inches 
B)  22.3 square inches 
C)  158.3 square inches 
D)  633.1 square inches 
A)  89.2 square inches 
B)  22.3 square inches 
C)  158.3 square inches 
D)  633.1 square inches

Question 14

A ssume all variables represent nonnegative real numbers.
-$4 \sqrt{3}(\sqrt{11}+\sqrt{3})$

Accepted Answer

A)  $4 \sqrt{33}+12$ 
B)  $4 \sqrt{33}+3$ 
C)  $4 \sqrt{11}+3$ 
D)  $12 \sqrt{11}+12$ 
A)  $4 \sqrt{33}+12$ 
B)  $4 \sqrt{33}+3$ 
C)  $4 \sqrt{11}+3$ 
D)  $12 \sqrt{11}+12$

Question 15

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers.
-$\left(4 x^{4} y^{4}\right)^{1 / 2}$

Accepted Answer

A)  $2 x^{4} y^{2}$ 
B)  $2 x^{2} y$ 
C)  $2 x^{2} y^{2}$ 
D)  $x^{2} y^{2}$ 
A)  $2 x^{4} y^{2}$ 
B)  $2 x^{2} y$ 
C)  $2 x^{2} y^{2}$ 
D)  $x^{2} y^{2}$

Question 16

Approximate to the nearest thousandth, using a calculator
-$-\sqrt{9791}$

Accepted Answer

A)  -98.949 
B)  -98.946 
C)  -98.954 
D)  -9791.000 
A)  -98.949 
B)  -98.946 
C)  -98.954 
D)  -9791.000

Question 17

$\sqrt[3]{32}$

Accepted Answer

A)  $4 \sqrt{2}$ 
B)  $2+\sqrt[3]{4}$ 
C)  $2 \sqrt[3]{4}$ 
D)  Not a real number 
A)  $4 \sqrt{2}$ 
B)  $2+\sqrt[3]{4}$ 
C)  $2 \sqrt[3]{4}$ 
D)  Not a real number

Question 18

Multiply
-$(7 \sqrt{7}+5 \sqrt{3})(8 \sqrt{7}+7 \sqrt{3})$

Accepted Answer

A)  $56 \sqrt{7}+35 \sqrt{3}+89 \sqrt{21}$ 
B)  $497+89 \sqrt{21}$ 
C)  $56 \sqrt{7}+35 \sqrt{3}$ 
D)  $287+89 \sqrt{21}$ 
A)  $56 \sqrt{7}+35 \sqrt{3}+89 \sqrt{21}$ 
B)  $497+89 \sqrt{21}$ 
C)  $56 \sqrt{7}+35 \sqrt{3}$ 
D)  $287+89 \sqrt{21}$

Question 19

The length of the diagonal of a rectangle is given by $D=\sqrt{L^{2}+W^{2}}$ where $L$ and $W$ are the length and width of the rectangle. What is the length of the diagonal, $D$, of a rectangle that is 73 inches long and 45 inches wide? Round your answer to the nearest tenth of an inch, if necessary.

Accepted Answer

A)  85.8 inches 
B)  57.3 inches 
C)  57.5 inches 
D)  10.9 inches 
A)  85.8 inches 
B)  57.3 inches 
C)  57.5 inches 
D)  10.9 inches

Question 20

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers.
-$\left(x^{10} y^{4} z^{8}\right)^{1 / 2}$

Accepted Answer

A)  $x^{5} y^{2} z^{4}$ 
B)  $x^{5} y^{2} z^{4} \sqrt{x y z}$ 
C)  $x^{10} y^{4} z^{4}$ 
D)  $\sqrt{x^{5} y^{2} z^{4}}$ 
A)  $x^{5} y^{2} z^{4}$ 
B)  $x^{5} y^{2} z^{4} \sqrt{x y z}$ 
C)  $x^{10} y^{4} z^{4}$ 
D)  $\sqrt{x^{5} y^{2} z^{4}}$

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - $\sqrt{\frac{81}{10}}$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $625^{5 / 4}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $x^{1 / 7} \cdot x^{6 / 7}$

olve. Check for extraneous solutions. - $\sqrt[4]{2 \mathrm{x}-2}+7=19$

$\mathrm{i}^{3}=-\mathrm{i}$

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

Rationalize the denominator and simplify. - $\frac{\sqrt{5}}{5 \sqrt{3}-\sqrt{5}}$

Simplify by rationalizing the denominator. Write your answer in a + bi form. - $\frac{4+3 i}{5+2 i}$

Find the sum graphically - $(2+4 i)+(3+2 i)$

If $a>0$ and $b>0$ , then $\sqrt{-a} \cdot \sqrt{b}=i \sqrt{a b}$ .

Multiply - $(7+\sqrt{3})^{2}$

$\mathrm{i}^{7}$

The radius of a sphere depends on its surface area, $S$ , and is given by the formula $r=\sqrt{\frac{\mathrm{S}}{4 \pi}}$ What is the surface area of a sphere with radius of 7.1 inches? Use 3.14 for $\pi$ . Round to the nearest tenth of a square inch.

A ssume all variables represent nonnegative real numbers. - $4 \sqrt{3}(\sqrt{11}+\sqrt{3})$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $\left(4 x^{4} y^{4}\right)^{1 / 2}$

Approximate to the nearest thousandth, using a calculator - $-\sqrt{9791}$

$\sqrt[3]{32}$

Multiply - $(7 \sqrt{7}+5 \sqrt{3})(8 \sqrt{7}+7 \sqrt{3})$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $\left(x^{10} y^{4} z^{8}\right)^{1 / 2}$

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

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - 8110\sqrt{\frac{81}{10}}1081​​

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - 6255/4625^{5 / 4}6255/4

Simplify the expression. Assume all variables represent nonnegative real numbers. - x1/7⋅x6/7x^{1 / 7} \cdot x^{6 / 7}x1/7⋅x6/7

olve. Check for extraneous solutions. - 2x−24+7=19\sqrt[4]{2 \mathrm{x}-2}+7=1942x−2​+7=19

i3=−i\mathrm{i}^{3}=-\mathrm{i}i3=−i

Solve. Check for extraneous solutions. - 2x+3−x+1=1\sqrt{2 \mathrm{x}+3}-\sqrt{\mathrm{x}+1}=12x+3​−x+1​=1

Rationalize the denominator and simplify. - 553−5\frac{\sqrt{5}}{5 \sqrt{3}-\sqrt{5}}53​−5​5​​

Simplify by rationalizing the denominator. Write your answer in a + bi form. - 4+3i5+2i\frac{4+3 i}{5+2 i}5+2i4+3i​

Find the sum graphically - (2+4i)+(3+2i)(2+4 i)+(3+2 i)(2+4i)+(3+2i)

If a>0a>0a>0 and b>0b>0b>0 , then −a⋅b=iab\sqrt{-a} \cdot \sqrt{b}=i \sqrt{a b}−a​⋅b​=iab​ .

Multiply - (7+3)2(7+\sqrt{3})^{2}(7+3​)2

i7\mathrm{i}^{7}i7

The radius of a sphere depends on its surface area, SSS , and is given by the formula r=S4πr=\sqrt{\frac{\mathrm{S}}{4 \pi}}r=4πS​​ What is the surface area of a sphere with radius of 7.1 inches? Use 3.14 for π\piπ . Round to the nearest tenth of a square inch.

A ssume all variables represent nonnegative real numbers. - 43(11+3)4 \sqrt{3}(\sqrt{11}+\sqrt{3})43​(11​+3​)

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - (4x4y4)1/2\left(4 x^{4} y^{4}\right)^{1 / 2}(4x4y4)1/2

Approximate to the nearest thousandth, using a calculator - −9791-\sqrt{9791}−9791​

323\sqrt[3]{32}332​

Multiply - (77+53)(87+73)(7 \sqrt{7}+5 \sqrt{3})(8 \sqrt{7}+7 \sqrt{3})(77​+53​)(87​+73​)

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - (x10y4z8)1/2\left(x^{10} y^{4} z^{8}\right)^{1 / 2}(x10y4z8)1/2

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

Rationalize the denominator and simplify. A ssume all variables represent nonnegative real numbers. - $\sqrt{\frac{81}{10}}$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $625^{5 / 4}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $x^{1 / 7} \cdot x^{6 / 7}$

olve. Check for extraneous solutions. - $\sqrt[4]{2 \mathrm{x}-2}+7=19$

$\mathrm{i}^{3}=-\mathrm{i}$

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

Rationalize the denominator and simplify. - $\frac{\sqrt{5}}{5 \sqrt{3}-\sqrt{5}}$

Simplify by rationalizing the denominator. Write your answer in a + bi form. - $\frac{4+3 i}{5+2 i}$

Find the sum graphically - $(2+4 i)+(3+2 i)$

If $a>0$ and $b>0$ , then $\sqrt{-a} \cdot \sqrt{b}=i \sqrt{a b}$ .

Multiply - $(7+\sqrt{3})^{2}$

$\mathrm{i}^{7}$

The radius of a sphere depends on its surface area, $S$ , and is given by the formula $r=\sqrt{\frac{\mathrm{S}}{4 \pi}}$ What is the surface area of a sphere with radius of 7.1 inches? Use 3.14 for $\pi$ . Round to the nearest tenth of a square inch.

A ssume all variables represent nonnegative real numbers. - $4 \sqrt{3}(\sqrt{11}+\sqrt{3})$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $\left(4 x^{4} y^{4}\right)^{1 / 2}$

Approximate to the nearest thousandth, using a calculator - $-\sqrt{9791}$

$\sqrt[3]{32}$

Multiply - $(7 \sqrt{7}+5 \sqrt{3})(8 \sqrt{7}+7 \sqrt{3})$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $\left(x^{10} y^{4} z^{8}\right)^{1 / 2}$