Question 1

Find two imaginary numbers whose product is - 99.

Accepted Answer

Answers may vary. On

Question 2

$(1+3 \mathrm{i}) \div(5+6 \mathrm{i})$

Accepted Answer

A)  $\frac{23}{61}+\frac{9}{61} \mathrm{i}$ 
B)  $\frac{13}{11}+\frac{9}{11} \mathrm{i}$ 
C)  $-\frac{13}{61}-\frac{21}{61} \mathrm{i}$ 
D)  $-\frac{23}{11}+\frac{9}{11} \mathrm{i}$ 
A)  $\frac{23}{61}+\frac{9}{61} \mathrm{i}$ 
B)  $\frac{13}{11}+\frac{9}{11} \mathrm{i}$ 
C)  $-\frac{13}{61}-\frac{21}{61} \mathrm{i}$ 
D)  $-\frac{23}{11}+\frac{9}{11} \mathrm{i}$

Question 3

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers.
-$\left(x^{3}\right)^{8 / 3}$

Accepted Answer

A)  $x^{9}$ 
B)  $x^{3}$ 
C)  $x^{4}$ 
D)  $x^{8}$ 
A)  $x^{9}$ 
B)  $x^{3}$ 
C)  $x^{4}$ 
D)  $x^{8}$

Question 4

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

Accepted Answer

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

Question 5

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$\sqrt{72 x^{2}}$

Accepted Answer

A)  $6 \sqrt{2 x}$ 
B)  $72 \mathrm{x}$ 
C)  $6 x$ 
D)  $6 x \sqrt{2}$ 
A)  $6 \sqrt{2 x}$ 
B)  $72 \mathrm{x}$ 
C)  $6 x$ 
D)  $6 x \sqrt{2}$

Question 6

Simplify the radical expression. If appropriate, include absolute values.
-$-\sqrt[4]{x^{28}}$

Accepted Answer

A)  $x^{7}$ 
B)  $-x^{7}$ 
C)  $\left|-x^{7}\right|$ 
D)  $-\left|x^{7}\right|$ 
A)  $x^{7}$ 
B)  $-x^{7}$ 
C)  $\left|-x^{7}\right|$ 
D)  $-\left|x^{7}\right|$

Question 7

olve. Check for extraneous solutions.
-$\sqrt[4]{\mathrm{x}-1}+6=0$

Accepted Answer

A)  $\{-1296\}$ 
B)  $\{-6\}$ 
C)  $\{1296\}$ 
D)  $\varnothing$ 
A)  $\{-1296\}$ 
B)  $\{-6\}$ 
C)  $\{1296\}$ 
D)  $\varnothing$

Question 8

Multiply the conjugates.
-$(\sqrt{11}-\sqrt{2})(\sqrt{11}+\sqrt{2})$

Accepted Answer

A)  9 
B)  13 
C)  $13-2 \sqrt{22}$ 
D)  $13+2 \sqrt{22}$ 
A)  9 
B)  13 
C)  $13-2 \sqrt{22}$ 
D)  $13+2 \sqrt{22}$

Question 9

Multiply.
-$\sqrt{-19} \cdot \sqrt{-6}$

Accepted Answer

A)  $-\sqrt{114}$ 
B)  $\sqrt{114}$ 
C)  $-\sqrt{114} i$ 
D)  $\sqrt{114} \mathrm{i}$ 
A)  $-\sqrt{114}$ 
B)  $\sqrt{114}$ 
C)  $-\sqrt{114} i$ 
D)  $\sqrt{114} \mathrm{i}$

Question 10

Simplify the expression. Assume all variables represent nonnegative real numbers.
-$\left(r^{1 / 4} s^{1 / 4}\right)^{2}$

Accepted Answer

A)  $\mathrm{r}^{1 / 8_{\mathrm{S}} 1 / 8}$ 
B)  $r^{1 / 16} s^{1 / 16}$ 
C)  $\mathrm{r}^{1 / 2} \mathrm{~s}^{1 / 2}$ 
D)  $r^{2} s^{2}$ 
A)  $\mathrm{r}^{1 / 8_{\mathrm{S}} 1 / 8}$ 
B)  $r^{1 / 16} s^{1 / 16}$ 
C)  $\mathrm{r}^{1 / 2} \mathrm{~s}^{1 / 2}$ 
D)  $r^{2} s^{2}$

Question 11

Explain in your own words why $\sqrt{\mathrm{a}^{2}} \neq \mathrm{a}$ when a is negative.

Accepted Answer

@#LAT-DLM& denotes the princip

Question 12

Simplify the radical expression. Assume all variables represent nonnegative real numbers.
-$-\sqrt[3]{64}$

Accepted Answer

A)  16 
B)  -4 
C)  4 
D)  - 64 
A)  16 
B)  -4 
C)  4 
D)  - 64

Question 13

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

-$5 \sqrt{\mathrm{r}}+2 \sqrt{\mathrm{r}}$

Accepted Answer

A)  $7 \sqrt{\mathrm{r}}$ 
B)  $\sqrt{\mathrm{r}}$ 
C)  $6 \sqrt{\mathrm{r}}$ 
D)  $8 \sqrt{r}$ 
A)  $7 \sqrt{\mathrm{r}}$ 
B)  $\sqrt{\mathrm{r}}$ 
C)  $6 \sqrt{\mathrm{r}}$ 
D)  $8 \sqrt{r}$

Question 14

Simplify the radical expression. Indicate if the expression is not a real number.
-$\sqrt{\frac{81}{16}}$

Accepted Answer

A)  $\frac{\sqrt{9}}{4}$ 
B)  $\frac{\sqrt{9}}{\sqrt{4}}$ 
C)  $\frac{9}{4}$ 
D)  2 
A)  $\frac{\sqrt{9}}{4}$ 
B)  $\frac{\sqrt{9}}{\sqrt{4}}$ 
C)  $\frac{9}{4}$ 
D)  2

Question 15

A ssume all variables represent nonnegative real numbers.
-$\sqrt{2}(\sqrt{72}-\sqrt{2})$

Accepted Answer

A)  14 
B)  $12-\sqrt{2}$ 
C)  10 
D)  $2 \sqrt{6}-2$ 
A)  14 
B)  $12-\sqrt{2}$ 
C)  10 
D)  $2 \sqrt{6}-2$

Question 16

Simplify. Assume all variables represent nonnegative values.
-$\frac{\sqrt{30 \mathrm{ab}^{3}}}{\sqrt{6 \mathrm{a}}}$

Accepted Answer

A)  $b^{2} \sqrt{5 b}$ 
B)  $b^{2} \sqrt{5 a b}$ 
C)  $b^{2} \sqrt{30 b}$ 
D)  $b \sqrt{5 b}$ 
A)  $b^{2} \sqrt{5 b}$ 
B)  $b^{2} \sqrt{5 a b}$ 
C)  $b^{2} \sqrt{30 b}$ 
D)  $b \sqrt{5 b}$

Question 17

For the function $f(x)=\sqrt[3]{6 x+6}+2$, find all values $x$ for which $f(x)=5$.

Accepted Answer

A)  $3 \frac{1}{2}$ 
B)  $19 \frac{1}{2}$ 
C)  $\frac{1}{2}$ 
D)  $\sqrt[3]{36}$ 
A)  $3 \frac{1}{2}$ 
B)  $19 \frac{1}{2}$ 
C)  $\frac{1}{2}$ 
D)  $\sqrt[3]{36}$

Question 18

Add or subtract the complex numbers
-$(6-5 \mathrm{i})+(4+3 \mathrm{i})$

Accepted Answer

A)  $-10+2 \mathrm{i}$ 
B)  $2+8 \mathrm{i}$ 
C)  $10+2 \mathrm{i}$ 
D)  $10-2 \mathrm{i}$ 
A)  $-10+2 \mathrm{i}$ 
B)  $2+8 \mathrm{i}$ 
C)  $10+2 \mathrm{i}$ 
D)  $10-2 \mathrm{i}$

Question 19

Simplify the expression. Assume all variables represent nonnegative real numbers.
-$\frac{y^{7 / 8}}{y^{3 / 8}}$

Accepted Answer

A)  y 
B)  $y^{-1 / 2}$ 
C)  $y^{7 / 8}$ 
D)  $y^{1 / 2}$ 
A)  y 
B)  $y^{-1 / 2}$ 
C)  $y^{7 / 8}$ 
D)  $y^{1 / 2}$

Question 20

Evaluate the radical function at the given value of the variable.
-$f(x)=\sqrt{x^{2}+2 x+1}$; find $f(7)$.

Accepted Answer

A)  7 
B)  6 
C)  8 
D)  5 
A)  7 
B)  6 
C)  8 
D)  5

Find two imaginary numbers whose product is - 99.

$(1+3 \mathrm{i}) \div(5+6 \mathrm{i})$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $\left(x^{3}\right)^{8 / 3}$

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

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt{72 x^{2}}$

Simplify the radical expression. If appropriate, include absolute values. - $-\sqrt[4]{x^{28}}$

olve. Check for extraneous solutions. - $\sqrt[4]{\mathrm{x}-1}+6=0$

Multiply the conjugates. - $(\sqrt{11}-\sqrt{2})(\sqrt{11}+\sqrt{2})$

Multiply. - $\sqrt{-19} \cdot \sqrt{-6}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\left(r^{1 / 4} s^{1 / 4}\right)^{2}$

Explain in your own words why $\sqrt{\mathrm{a}^{2}} \neq \mathrm{a}$ when a is negative.

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $-\sqrt[3]{64}$

Add or subtract. Assume all variables represent nonnegative real numbers. - $5 \sqrt{\mathrm{r}}+2 \sqrt{\mathrm{r}}$

Simplify the radical expression. Indicate if the expression is not a real number. - $\sqrt{\frac{81}{16}}$

A ssume all variables represent nonnegative real numbers. - $\sqrt{2}(\sqrt{72}-\sqrt{2})$

Simplify. Assume all variables represent nonnegative values. - $\frac{\sqrt{30 \mathrm{ab}^{3}}}{\sqrt{6 \mathrm{a}}}$

For the function $f(x)=\sqrt[3]{6 x+6}+2$ , find all values $x$ for which $f(x)=5$ .

Add or subtract the complex numbers - $(6-5 \mathrm{i})+(4+3 \mathrm{i})$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\frac{y^{7 / 8}}{y^{3 / 8}}$

Evaluate the radical function at the given value of the variable. - $f(x)=\sqrt{x^{2}+2 x+1}$ ; find $f(7)$ .

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

Find two imaginary numbers whose product is - 99.

(1+3i)÷(5+6i)(1+3 \mathrm{i}) \div(5+6 \mathrm{i})(1+3i)÷(5+6i)

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - (x3)8/3\left(x^{3}\right)^{8 / 3}(x3)8/3

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

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - 72x2\sqrt{72 x^{2}}72x2​

Simplify the radical expression. If appropriate, include absolute values. - −x284-\sqrt[4]{x^{28}}−4x28​

olve. Check for extraneous solutions. - x−14+6=0\sqrt[4]{\mathrm{x}-1}+6=04x−1​+6=0

Multiply the conjugates. - (11−2)(11+2)(\sqrt{11}-\sqrt{2})(\sqrt{11}+\sqrt{2})(11​−2​)(11​+2​)

Multiply. - −19⋅−6\sqrt{-19} \cdot \sqrt{-6}−19​⋅−6​

Simplify the expression. Assume all variables represent nonnegative real numbers. - (r1/4s1/4)2\left(r^{1 / 4} s^{1 / 4}\right)^{2}(r1/4s1/4)2

Explain in your own words why a2≠a\sqrt{\mathrm{a}^{2}} \neq \mathrm{a}a2​=a when a is negative.

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - −643-\sqrt[3]{64}−364​

Add or subtract. Assume all variables represent nonnegative real numbers. - 5r+2r5 \sqrt{\mathrm{r}}+2 \sqrt{\mathrm{r}}5r​+2r​

Simplify the radical expression. Indicate if the expression is not a real number. - 8116\sqrt{\frac{81}{16}}1681​​

A ssume all variables represent nonnegative real numbers. - 2(72−2)\sqrt{2}(\sqrt{72}-\sqrt{2})2​(72​−2​)

Simplify. Assume all variables represent nonnegative values. - 30ab36a\frac{\sqrt{30 \mathrm{ab}^{3}}}{\sqrt{6 \mathrm{a}}}6a​30ab3​​

For the function f(x)=6x+63+2f(x)=\sqrt[3]{6 x+6}+2f(x)=36x+6​+2 , find all values xxx for which f(x)=5f(x)=5f(x)=5 .

Add or subtract the complex numbers - (6−5i)+(4+3i)(6-5 \mathrm{i})+(4+3 \mathrm{i})(6−5i)+(4+3i)

Simplify the expression. Assume all variables represent nonnegative real numbers. - y7/8y3/8\frac{y^{7 / 8}}{y^{3 / 8}}y3/8y7/8​

Evaluate the radical function at the given value of the variable. - f(x)=x2+2x+1f(x)=\sqrt{x^{2}+2 x+1}f(x)=x2+2x+1​ ; find f(7)f(7)f(7) .

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

$(1+3 \mathrm{i}) \div(5+6 \mathrm{i})$

Rewrite as a radical expression and simplify if possible. Assume all variables represent nonnegative real numbers. - $\left(x^{3}\right)^{8 / 3}$

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

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $\sqrt{72 x^{2}}$

Simplify the radical expression. If appropriate, include absolute values. - $-\sqrt[4]{x^{28}}$

olve. Check for extraneous solutions. - $\sqrt[4]{\mathrm{x}-1}+6=0$

Multiply the conjugates. - $(\sqrt{11}-\sqrt{2})(\sqrt{11}+\sqrt{2})$

Multiply. - $\sqrt{-19} \cdot \sqrt{-6}$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\left(r^{1 / 4} s^{1 / 4}\right)^{2}$

Explain in your own words why $\sqrt{\mathrm{a}^{2}} \neq \mathrm{a}$ when a is negative.

Simplify the radical expression. Assume all variables represent nonnegative real numbers. - $-\sqrt[3]{64}$

Add or subtract. Assume all variables represent nonnegative real numbers. - $5 \sqrt{\mathrm{r}}+2 \sqrt{\mathrm{r}}$

Simplify the radical expression. Indicate if the expression is not a real number. - $\sqrt{\frac{81}{16}}$

A ssume all variables represent nonnegative real numbers. - $\sqrt{2}(\sqrt{72}-\sqrt{2})$

Simplify. Assume all variables represent nonnegative values. - $\frac{\sqrt{30 \mathrm{ab}^{3}}}{\sqrt{6 \mathrm{a}}}$

For the function $f(x)=\sqrt[3]{6 x+6}+2$ , find all values $x$ for which $f(x)=5$ .

Add or subtract the complex numbers - $(6-5 \mathrm{i})+(4+3 \mathrm{i})$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\frac{y^{7 / 8}}{y^{3 / 8}}$

Evaluate the radical function at the given value of the variable. - $f(x)=\sqrt{x^{2}+2 x+1}$ ; find $f(7)$ .