Question 1

Solve. Check for extraneous solutions.
-$\left(x^{2}-7 x+14\right)^{1 / 2}-1=1$

Accepted Answer

A)  $\{-2,-5\}$ 
B)  $\{2,-5\}$. 
C)  $\{2,5\}$ 
D)  $\varnothing$ 
A)  $\{-2,-5\}$ 
B)  $\{2,-5\}$. 
C)  $\{2,5\}$ 
D)  $\varnothing$

Question 2

Simplify the expression. Assume all variables represent nonnegative real numbers.
-$\left(\mathrm{x}^{2 / 3}\right)^{4 / 7}$

Accepted Answer

A)  $x^{8 / 21}$ 
B)  $x^{26 / 21}$ 
C)  $x^{8 / 7}$ 
D)  $x^{21 / 8}$ 
A)  $x^{8 / 21}$ 
B)  $x^{26 / 21}$ 
C)  $x^{8 / 7}$ 
D)  $x^{21 / 8}$

Question 3

$-3 \sqrt{2}-9 \sqrt{18}$

Accepted Answer

A)  $-30 \sqrt{2}$ 
B)  $-12 \sqrt{2}$ 
C)  $30 \sqrt{2}$ 
D)  $-24 \sqrt{2}$ 
A)  $-30 \sqrt{2}$ 
B)  $-12 \sqrt{2}$ 
C)  $30 \sqrt{2}$ 
D)  $-24 \sqrt{2}$

Question 4

Simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$, and evaluate as $h$ approaches 0 to find the rate of change of $f(x)$.
-$f(x)=\sqrt{5 x}$

Accepted Answer

A)  $\frac{5}{2 \sqrt{5 x}}$ 
B)  $-\frac{2}{\sqrt{5 x}}$ 
C)  $-\frac{5}{2 \sqrt{5 x}}$ 
D)  $\frac{1}{\sqrt{5 x}}$ 
A)  $\frac{5}{2 \sqrt{5 x}}$ 
B)  $-\frac{2}{\sqrt{5 x}}$ 
C)  $-\frac{5}{2 \sqrt{5 x}}$ 
D)  $\frac{1}{\sqrt{5 x}}$

Question 5

A ssume all variables represent nonnegative real numbers.
-$\sqrt{15} \cdot \sqrt{48}$

Accepted Answer

A)  $20 \sqrt{3}$ 
B)  $-12 \sqrt{5}$ 
C)  $-20 \sqrt{3}$ 
D)  $12 \sqrt{5}$ 
A)  $20 \sqrt{3}$ 
B)  $-12 \sqrt{5}$ 
C)  $-20 \sqrt{3}$ 
D)  $12 \sqrt{5}$

Question 6

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

Accepted Answer

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

Question 7

$(1-3 i) \div(5-7 i)$

Accepted Answer

A)  $\frac{2}{3}-\frac{1}{6} \mathrm{i}$ 
B)  $-\frac{13}{24}-\frac{1}{6} \mathrm{i}$ 
C)  $\frac{13}{37}-\frac{4}{37} \mathrm{i}$ 
D)  $-\frac{16}{37}+\frac{22}{37} \mathrm{i}$ 
A)  $\frac{2}{3}-\frac{1}{6} \mathrm{i}$ 
B)  $-\frac{13}{24}-\frac{1}{6} \mathrm{i}$ 
C)  $\frac{13}{37}-\frac{4}{37} \mathrm{i}$ 
D)  $-\frac{16}{37}+\frac{22}{37} \mathrm{i}$

Question 8

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers.
-$\left(\sqrt[9]{5 x^{4} y}\right)^{7}$

Accepted Answer

A)  $\left(5 x^{4} y\right)^{7 / 9}$ 
B)  $(5 x y)^{19}$ 
C)  $\left(5 x^{4} y\right)^{9 / 7}$ 
D)  $\left(5 x^{4} y\right)^{2}$ 
A)  $\left(5 x^{4} y\right)^{7 / 9}$ 
B)  $(5 x y)^{19}$ 
C)  $\left(5 x^{4} y\right)^{9 / 7}$ 
D)  $\left(5 x^{4} y\right)^{2}$

Question 9

$11 \sqrt[3]{3}+15 \sqrt[3]{3}$

Accepted Answer

A)  $26 \sqrt[3]{6}$ 
B)  $26 \sqrt[3]{9}$ 
C)  $26 \sqrt[3]{3}$ 
D)  $4 \sqrt[3]{3}$ 
A)  $26 \sqrt[3]{6}$ 
B)  $26 \sqrt[3]{9}$ 
C)  $26 \sqrt[3]{3}$ 
D)  $4 \sqrt[3]{3}$

Question 10

olve. Check for extraneous solutions.
-$\sqrt{8 \mathrm{x}-5}-2=0$

Accepted Answer

A)  $\left\{\frac{7}{8}\right\}$ 
B)  $\left\{\frac{9}{8}\right\}$ 
C)  $\{4\}$ 
D)  $\varnothing$ 
A)  $\left\{\frac{7}{8}\right\}$ 
B)  $\left\{\frac{9}{8}\right\}$ 
C)  $\{4\}$ 
D)  $\varnothing$

Question 11

Multiply. Write your answer in a +bi form.
-$(7-7 i)(8+9 i)$

Accepted Answer

A)  $119-7 \mathrm{i}$ 
B)  $-63 i^{2}+7 i+56$ 
C)  -7 - 119i 
D)  $119+7 \mathrm{i}$ 
A)  $119-7 \mathrm{i}$ 
B)  $-63 i^{2}+7 i+56$ 
C)  -7 - 119i 
D)  $119+7 \mathrm{i}$

Question 12

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

-$\sqrt{5 a}-3 \sqrt{125 a}-2 \sqrt{20 a}$

Accepted Answer

A)  $-18 \sqrt{5 a}$ 
B)  $-5 \sqrt{5 a}$ 
C)  $-5 \sqrt{150 \mathrm{a}}$ 
D)  $-18 \sqrt{150 a}$ 
A)  $-18 \sqrt{5 a}$ 
B)  $-5 \sqrt{5 a}$ 
C)  $-5 \sqrt{150 \mathrm{a}}$ 
D)  $-18 \sqrt{150 a}$

Question 13

Find the missing number
-$\sqrt{?}=12 \mathrm{y}^{3}$

Accepted Answer

A)  $12 y^{3}$ 
B)  $12 y^{6}$ 
C)  $144 y^{6}$ 
D)  $144 y^{3}$ 
A)  $12 y^{3}$ 
B)  $12 y^{6}$ 
C)  $144 y^{6}$ 
D)  $144 y^{3}$

Question 14

Solve. Check for extraneous solutions.
-$\sqrt{2 \mathrm{x}+5}-\sqrt{\mathrm{x}-2}=3$

Accepted Answer

A)  $\{3,8\}$ 
B)  $\{-2\}$ 
C)  $\{2\}$. 
D)  $\{2,38\}$ 
A)  $\{3,8\}$ 
B)  $\{-2\}$ 
C)  $\{2\}$. 
D)  $\{2,38\}$

Question 15

$(\sqrt{6}-2)(\sqrt{7}-4)$

Accepted Answer

A)  $\sqrt{42}-4 \sqrt{6}-2 \sqrt{7}+8$ 
B)  $\sqrt{42}-6 \sqrt{7}+8$ 
C)  $-5 \sqrt{42}+8$ 
D)  $\sqrt{42}+8$ 
A)  $\sqrt{42}-4 \sqrt{6}-2 \sqrt{7}+8$ 
B)  $\sqrt{42}-6 \sqrt{7}+8$ 
C)  $-5 \sqrt{42}+8$ 
D)  $\sqrt{42}+8$

Question 16

A ssume all variables represent nonnegative real numbers.
-$\sqrt[3]{112} \cdot \sqrt[3]{16}$

Accepted Answer

A)  $4 \sqrt[3]{28}$ 
B)  $8 \sqrt[3]{28}$ 
C)  $8 \sqrt[3]{12}$ 
D)  $4 \sqrt[3]{20}$ 
A)  $4 \sqrt[3]{28}$ 
B)  $8 \sqrt[3]{28}$ 
C)  $8 \sqrt[3]{12}$ 
D)  $4 \sqrt[3]{20}$

Question 17

For the function $f(x)=2 \sqrt{x-3}-2 \sqrt{2 x-4}$, find all values $x$ for which $f(x)=2$.

Accepted Answer

A)  2 
B)  4 
C)  -2 
D)  $\varnothing$ 
A)  2 
B)  4 
C)  -2 
D)  $\varnothing$

Question 18

olve. Check for extraneous solutions.
-$\sqrt{7 \mathrm{x}-6}=6$

Accepted Answer

A)  $\{36\}$ 
B)  $\{6\}$ 
C)  $\left\{\frac{36}{7}\right\}$ 
D)  $\left\{\frac{30}{7}\right\}$ 
A)  $\{36\}$ 
B)  $\{6\}$ 
C)  $\left\{\frac{36}{7}\right\}$ 
D)  $\left\{\frac{30}{7}\right\}$

Question 19

Find the missing complex number
-$(3-5 \mathrm{i})+?=8+2 \mathrm{i}$

Accepted Answer

A)  $-8-2 \mathrm{i}$ 
B)  8 - $2 \mathrm{i}$ 
C)  $5+7 i$ 
D)  $-2+12 i$ 
A)  $-8-2 \mathrm{i}$ 
B)  8 - $2 \mathrm{i}$ 
C)  $5+7 i$ 
D)  $-2+12 i$

Question 20

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

Accepted Answer

A)  $9-4 \sqrt{2}$ 
B)  $9+4 \sqrt{2}$ 
C)  $17-12 \sqrt{2}$ 
D)  $17+12 \sqrt{2}$ 
A)  $9-4 \sqrt{2}$ 
B)  $9+4 \sqrt{2}$ 
C)  $17-12 \sqrt{2}$ 
D)  $17+12 \sqrt{2}$

Solve. Check for extraneous solutions. - $\left(x^{2}-7 x+14\right)^{1 / 2}-1=1$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\left(\mathrm{x}^{2 / 3}\right)^{4 / 7}$

$-3 \sqrt{2}-9 \sqrt{18}$

Simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ , and evaluate as $h$ approaches 0 to find the rate of change of $f(x)$ . - $f(x)=\sqrt{5 x}$

A ssume all variables represent nonnegative real numbers. - $\sqrt{15} \cdot \sqrt{48}$

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

$(1-3 i) \div(5-7 i)$

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - $\left(\sqrt[9]{5 x^{4} y}\right)^{7}$

$11 \sqrt[3]{3}+15 \sqrt[3]{3}$

olve. Check for extraneous solutions. - $\sqrt{8 \mathrm{x}-5}-2=0$

Multiply. Write your answer in a +bi form. - $(7-7 i)(8+9 i)$

Add or subtract. Assume all variables represent nonnegative real numbers. - $\sqrt{5 a}-3 \sqrt{125 a}-2 \sqrt{20 a}$

Find the missing number - $\sqrt{?}=12 \mathrm{y}^{3}$

Solve. Check for extraneous solutions. - $\sqrt{2 \mathrm{x}+5}-\sqrt{\mathrm{x}-2}=3$

$(\sqrt{6}-2)(\sqrt{7}-4)$

A ssume all variables represent nonnegative real numbers. - $\sqrt[3]{112} \cdot \sqrt[3]{16}$

For the function $f(x)=2 \sqrt{x-3}-2 \sqrt{2 x-4}$ , find all values $x$ for which $f(x)=2$ .

olve. Check for extraneous solutions. - $\sqrt{7 \mathrm{x}-6}=6$

Find the missing complex number - $(3-5 \mathrm{i})+?=8+2 \mathrm{i}$

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

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

Solve. Check for extraneous solutions. - (x2−7x+14)1/2−1=1\left(x^{2}-7 x+14\right)^{1 / 2}-1=1(x2−7x+14)1/2−1=1

Simplify the expression. Assume all variables represent nonnegative real numbers. - (x2/3)4/7\left(\mathrm{x}^{2 / 3}\right)^{4 / 7}(x2/3)4/7

−32−918-3 \sqrt{2}-9 \sqrt{18}−32​−918​

Simplify the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ , and evaluate as hhh approaches 0 to find the rate of change of f(x)f(x)f(x) . - f(x)=5xf(x)=\sqrt{5 x}f(x)=5x​

A ssume all variables represent nonnegative real numbers. - 15⋅48\sqrt{15} \cdot \sqrt{48}15​⋅48​

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

(1−3i)÷(5−7i)(1-3 i) \div(5-7 i)(1−3i)÷(5−7i)

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - (5x4y9)7\left(\sqrt[9]{5 x^{4} y}\right)^{7}(95x4y​)7

1133+153311 \sqrt[3]{3}+15 \sqrt[3]{3}1133​+1533​

olve. Check for extraneous solutions. - 8x−5−2=0\sqrt{8 \mathrm{x}-5}-2=08x−5​−2=0

Multiply. Write your answer in a +bi form. - (7−7i)(8+9i)(7-7 i)(8+9 i)(7−7i)(8+9i)

Add or subtract. Assume all variables represent nonnegative real numbers. - 5a−3125a−220a\sqrt{5 a}-3 \sqrt{125 a}-2 \sqrt{20 a}5a​−3125a​−220a​

Find the missing number - ?=12y3\sqrt{?}=12 \mathrm{y}^{3}?​=12y3

Solve. Check for extraneous solutions. - 2x+5−x−2=3\sqrt{2 \mathrm{x}+5}-\sqrt{\mathrm{x}-2}=32x+5​−x−2​=3

(6−2)(7−4)(\sqrt{6}-2)(\sqrt{7}-4)(6​−2)(7​−4)

A ssume all variables represent nonnegative real numbers. - 1123⋅163\sqrt[3]{112} \cdot \sqrt[3]{16}3112​⋅316​

For the function f(x)=2x−3−22x−4f(x)=2 \sqrt{x-3}-2 \sqrt{2 x-4}f(x)=2x−3​−22x−4​ , find all values xxx for which f(x)=2f(x)=2f(x)=2 .

olve. Check for extraneous solutions. - 7x−6=6\sqrt{7 \mathrm{x}-6}=67x−6​=6

Find the missing complex number - (3−5i)+?=8+2i(3-5 \mathrm{i})+?=8+2 \mathrm{i}(3−5i)+?=8+2i

Multiply - (3−22)2(3-2 \sqrt{2})^{2}(3−22​)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

Solve. Check for extraneous solutions. - $\left(x^{2}-7 x+14\right)^{1 / 2}-1=1$

Simplify the expression. Assume all variables represent nonnegative real numbers. - $\left(\mathrm{x}^{2 / 3}\right)^{4 / 7}$

$-3 \sqrt{2}-9 \sqrt{18}$

Simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ , and evaluate as $h$ approaches 0 to find the rate of change of $f(x)$ . - $f(x)=\sqrt{5 x}$

A ssume all variables represent nonnegative real numbers. - $\sqrt{15} \cdot \sqrt{48}$

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

$(1-3 i) \div(5-7 i)$

Rewrite the radical expression using rational exponents. A ssume all variables represent nonnegative real numbers. - $\left(\sqrt[9]{5 x^{4} y}\right)^{7}$

$11 \sqrt[3]{3}+15 \sqrt[3]{3}$

olve. Check for extraneous solutions. - $\sqrt{8 \mathrm{x}-5}-2=0$

Multiply. Write your answer in a +bi form. - $(7-7 i)(8+9 i)$

Add or subtract. Assume all variables represent nonnegative real numbers. - $\sqrt{5 a}-3 \sqrt{125 a}-2 \sqrt{20 a}$

Find the missing number - $\sqrt{?}=12 \mathrm{y}^{3}$

Solve. Check for extraneous solutions. - $\sqrt{2 \mathrm{x}+5}-\sqrt{\mathrm{x}-2}=3$

$(\sqrt{6}-2)(\sqrt{7}-4)$

A ssume all variables represent nonnegative real numbers. - $\sqrt[3]{112} \cdot \sqrt[3]{16}$

For the function $f(x)=2 \sqrt{x-3}-2 \sqrt{2 x-4}$ , find all values $x$ for which $f(x)=2$ .

olve. Check for extraneous solutions. - $\sqrt{7 \mathrm{x}-6}=6$

Find the missing complex number - $(3-5 \mathrm{i})+?=8+2 \mathrm{i}$

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