Question 1

Add or subtract. Simplify by collecting like radical terms, if possible.
-$\sqrt{18}-3 \sqrt{200}-8 \sqrt{72}$

Accepted Answer

A)  $86 \sqrt{2}$ 
B)  $75 \sqrt{2}$ 
C)  $-75 \sqrt{2}$ 
D)  $-200 \sqrt{2}$ 
A)  $86 \sqrt{2}$ 
B)  $75 \sqrt{2}$ 
C)  $-75 \sqrt{2}$ 
D)  $-200 \sqrt{2}$

Question 2

Multiply and then, if possible, simplify by factoring.
-$\sqrt{64} \sqrt{4}$

Accepted Answer

A)  $4 \sqrt{16}$ 
B)  $4 \sqrt{4}$ 
C)  256 
D)  16 
A)  $4 \sqrt{16}$ 
B)  $4 \sqrt{4}$ 
C)  256 
D)  16

Question 3

Solve the problem.
-A retailer finds that total costs per day are given by $c=169 \sqrt{n}+196$, where $c$ is cost and $n$ is units sold. What is $\mathrm{c}$ when no units are sold?

Accepted Answer

A)  $\$ 196$ 
B)  $\$ 365$ 
C)  $\$ 182$ 
D)  $\$ 2366$ 
A)  $\$ 196$ 
B)  $\$ 365$ 
C)  $\$ 182$ 
D)  $\$ 2366$

Question 4

Decide whether or not the radical expression represents a real number.
-$\sqrt{-(-107)}$

Accepted Answer

A) True 
 B)False

Question 5

Provide an appropriate response.
-Explain why the equation $x^{2}=16$ has two real- number solutions, while the equation $\sqrt{\mathrm{x}}=4$ has only one real- number solution.

Accepted Answer

The answer of Provide an appropriate response.
-Explain why the equation...

Question 6

Use a calculator to approximate the square root. Round to three decimal places.
-$-\sqrt{0.00139}$

Accepted Answer

A)  -3.700 
B)  -0.004 
C)  -0.037 
D)  Not a real number 
A)  -3.700 
B)  -0.004 
C)  -0.037 
D)  Not a real number

Question 7

Solve the problem. Give an exact answer and an approximation to the nearest tenth.
-Below is a diagram of a water slide. How far is it along the ground from the end of the slide back to the base of the ladder that leads to the slide?

Accepted Answer

A)  $\sqrt{11} \mathrm{ft} \approx 3.3 \mathrm{ft}$ 
B)  $\sqrt{539} \mathrm{ft}=269.5 \mathrm{ft}$ 
C)  $\sqrt{1261} \mathrm{ft} \approx 35.5 \mathrm{ft}$ 
D)  $\sqrt{539} \mathrm{ft} \approx 23.2 \mathrm{ft}$ 
A)  $\sqrt{11} \mathrm{ft} \approx 3.3 \mathrm{ft}$ 
B)  $\sqrt{539} \mathrm{ft}=269.5 \mathrm{ft}$ 
C)  $\sqrt{1261} \mathrm{ft} \approx 35.5 \mathrm{ft}$ 
D)  $\sqrt{539} \mathrm{ft} \approx 23.2 \mathrm{ft}$

Question 8

Simplify by factoring.
-$\sqrt{(x-5)^{16}}$

Accepted Answer

A)  $x-5^{9}$ 
B)  $(x-5)^{8}$ 
C)  $(x-5)^{7}$ 
D)  $(x-5)^{8} \sqrt{(x-5)}$ 
A)  $x-5^{9}$ 
B)  $(x-5)^{8}$ 
C)  $(x-5)^{7}$ 
D)  $(x-5)^{8} \sqrt{(x-5)}$

Question 9

Identify the radicand.
-$6 \sqrt{x^{2}+2}$

Accepted Answer

A)  $6 \sqrt{x^{2}+2}$ 
B)  6 
C)  $x^{2}+2$ 
D)  $\sqrt{x^{2}+2}$ 
A)  $6 \sqrt{x^{2}+2}$ 
B)  6 
C)  $x^{2}+2$ 
D)  $\sqrt{x^{2}+2}$

Question 10

Simplify.
-$\sqrt{\frac{98 \mathrm{r}^{2}}{\mathrm{x}^{4}}}$

Accepted Answer

A)  $\frac{49 r \sqrt{2}}{x^{2}}$ 
B)  $\frac{r \sqrt{98}}{x^{2}}$ 
C)  $\frac{7 \sqrt{2 r^{2}}}{x^{2}}$ 
D)  $\frac{7 r \sqrt{2}}{x^{2}}$ 
A)  $\frac{49 r \sqrt{2}}{x^{2}}$ 
B)  $\frac{r \sqrt{98}}{x^{2}}$ 
C)  $\frac{7 \sqrt{2 r^{2}}}{x^{2}}$ 
D)  $\frac{7 r \sqrt{2}}{x^{2}}$

Question 11

Simplify.
-$\sqrt{225}$

Accepted Answer

A)  -112 
B)  15 
C)  -15 
D)  Not a real number 
A)  -112 
B)  15 
C)  -15 
D)  Not a real number

Question 12

Simplify.
-$\frac{\sqrt{5 t^{11}}}{\sqrt{80 t^{5}}}$

Accepted Answer

A)  $\sqrt{\frac{t^{3}}{4}}$ 
B)  $\frac{t^{6}}{4}$ 
C)  $\frac{t^{3}}{4}$ 
D)  $\frac{t^{3}}{\sqrt{4}}$ 
A)  $\sqrt{\frac{t^{3}}{4}}$ 
B)  $\frac{t^{6}}{4}$ 
C)  $\frac{t^{3}}{4}$ 
D)  $\frac{t^{3}}{\sqrt{4}}$

Question 13

Simplify by factoring.
-$\sqrt{25 m^{21}}$

Accepted Answer

A)  $5 \mathrm{~m}^{9} \sqrt{\mathrm{m}}$ 
B)  $5 \mathrm{~m}^{10} \sqrt{\mathrm{m}}$ 
C)  $5 m^{11}$ 
D)  $5 m^{10}$ 
A)  $5 \mathrm{~m}^{9} \sqrt{\mathrm{m}}$ 
B)  $5 \mathrm{~m}^{10} \sqrt{\mathrm{m}}$ 
C)  $5 m^{11}$ 
D)  $5 m^{10}$

Question 14

Add or subtract. Simplify by collecting like radical terms, if possible.
-$8 \sqrt{2}-5 \sqrt{50}$

Accepted Answer

A)  $3 \sqrt{2}$ 
B)  $-33 \sqrt{2}$ 
C)  $17 \sqrt{2}$ 
D)  $-17 \sqrt{2}$ 
A)  $3 \sqrt{2}$ 
B)  $-33 \sqrt{2}$ 
C)  $17 \sqrt{2}$ 
D)  $-17 \sqrt{2}$

Question 15

Divide and simplify.
-$\frac{\sqrt{6}}{\sqrt{150}}$

Accepted Answer

A)  $\frac{1}{5}$ 
B)  $\frac{\sqrt{6}}{5}$ 
C)  6 
D)  $5 \sqrt{6}$ 
A)  $\frac{1}{5}$ 
B)  $\frac{\sqrt{6}}{5}$ 
C)  6 
D)  $5 \sqrt{6}$

Question 16

Solve the equation.
-$\sqrt{\mathrm{x}^{2}-3}=\sqrt{\mathrm{x}+3}$

Accepted Answer

A)  No solution 
B)  $-2,3$ 
C)  3 
D)  3,3 
A)  No solution 
B)  $-2,3$ 
C)  3 
D)  3,3

Question 17

Solve the problem. Give an exact answer and an approximation to the nearest tenth.
-A boat travels $4 \mathrm{mi}$ south and then $6 \mathrm{mi}$ east. How far is the boat from its starting point?
  $\mathrm{A}=4 \mathrm{mi} \quad \mathrm{B}=6$

Accepted Answer

A)  $\sqrt{10} \mathrm{mi} \approx 3.2 \mathrm{mi}$ 
B)  $\sqrt{52} \mathrm{mi}=26 \mathrm{mi}$ 
C)  $\sqrt{22} \mathrm{mi} \approx 4.7 \mathrm{mi}$ 
D)  $\sqrt{52} \mathrm{mi} \approx 7.2 \mathrm{mi}$ 
A)  $\sqrt{10} \mathrm{mi} \approx 3.2 \mathrm{mi}$ 
B)  $\sqrt{52} \mathrm{mi}=26 \mathrm{mi}$ 
C)  $\sqrt{22} \mathrm{mi} \approx 4.7 \mathrm{mi}$ 
D)  $\sqrt{52} \mathrm{mi} \approx 7.2 \mathrm{mi}$

Question 18

Simplify by factoring.
-$\sqrt{175}$

Accepted Answer

A)  $7 \sqrt{5}$ 
B)  35 
C)  $5 \sqrt{7}$ 
D)  13 
A)  $7 \sqrt{5}$ 
B)  35 
C)  $5 \sqrt{7}$ 
D)  13

Question 19

Identify the radicand.
-$4 x \sqrt{y-5}$

Accepted Answer

A)  $y-5$ 
B)  $4 \mathrm{x}$ 
C)  $\sqrt{y-5}$ 
D)  $\mathrm{y}$ 
A)  $y-5$ 
B)  $4 \mathrm{x}$ 
C)  $\sqrt{y-5}$ 
D)  $\mathrm{y}$

Question 20

Solve the equation.
-$\sqrt{\mathrm{x}+6}+\sqrt{2-\mathrm{x}}=4$

Accepted Answer

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

Add or subtract. Simplify by collecting like radical terms, if possible. - $\sqrt{18}-3 \sqrt{200}-8 \sqrt{72}$

Multiply and then, if possible, simplify by factoring. - $\sqrt{64} \sqrt{4}$

Solve the problem. -A retailer finds that total costs per day are given by $c=169 \sqrt{n}+196$ , where $c$ is cost and $n$ is units sold. What is $\mathrm{c}$ when no units are sold?

Decide whether or not the radical expression represents a real number. - $\sqrt{-(-107)}$

Provide an appropriate response. -Explain why the equation $x^{2}=16$ has two real- number solutions, while the equation $\sqrt{\mathrm{x}}=4$ has only one real- number solution.

Use a calculator to approximate the square root. Round to three decimal places. - $-\sqrt{0.00139}$

Solve the problem. Give an exact answer and an approximation to the nearest tenth. -Below is a diagram of a water slide. How far is it along the ground from the end of the slide back to the base of the ladder that leads to the slide?

Simplify by factoring. - $\sqrt{(x-5)^{16}}$

Identify the radicand. - $6 \sqrt{x^{2}+2}$

Simplify. - $\sqrt{\frac{98 \mathrm{r}^{2}}{\mathrm{x}^{4}}}$

Simplify. - $\sqrt{225}$

Simplify. - $\frac{\sqrt{5 t^{11}}}{\sqrt{80 t^{5}}}$

Simplify by factoring. - $\sqrt{25 m^{21}}$

Add or subtract. Simplify by collecting like radical terms, if possible. - $8 \sqrt{2}-5 \sqrt{50}$

Divide and simplify. - $\frac{\sqrt{6}}{\sqrt{150}}$

Solve the equation. - $\sqrt{\mathrm{x}^{2}-3}=\sqrt{\mathrm{x}+3}$

Simplify by factoring. - $\sqrt{175}$

Identify the radicand. - $4 x \sqrt{y-5}$

Solve the equation. - $\sqrt{\mathrm{x}+6}+\sqrt{2-\mathrm{x}}=4$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Rational Expressions and Equations

Systems of Equations

Quadratic Equations

Equations of Lines and Simplifying Radical Expressions

Filters

Exam 8: Radical Expressions and Equations

Add or subtract. Simplify by collecting like radical terms, if possible. - 18−3200−872\sqrt{18}-3 \sqrt{200}-8 \sqrt{72}18​−3200​−872​

Multiply and then, if possible, simplify by factoring. - 644\sqrt{64} \sqrt{4}64​4​

Solve the problem. -A retailer finds that total costs per day are given by c=169n+196c=169 \sqrt{n}+196c=169n​+196 , where ccc is cost and nnn is units sold. What is c\mathrm{c}c when no units are sold?

Decide whether or not the radical expression represents a real number. - −(−107)\sqrt{-(-107)}−(−107)​

Provide an appropriate response. -Explain why the equation x2=16x^{2}=16x2=16 has two real- number solutions, while the equation x=4\sqrt{\mathrm{x}}=4x​=4 has only one real- number solution.

Use a calculator to approximate the square root. Round to three decimal places. - −0.00139-\sqrt{0.00139}−0.00139​

Solve the problem. Give an exact answer and an approximation to the nearest tenth. -Below is a diagram of a water slide. How far is it along the ground from the end of the slide back to the base of the ladder that leads to the slide?

Simplify by factoring. - (x−5)16\sqrt{(x-5)^{16}}(x−5)16​

Identify the radicand. - 6x2+26 \sqrt{x^{2}+2}6x2+2​

Simplify. - 98r2x4\sqrt{\frac{98 \mathrm{r}^{2}}{\mathrm{x}^{4}}}x498r2​​

Simplify. - 225\sqrt{225}225​

Simplify. - 5t1180t5\frac{\sqrt{5 t^{11}}}{\sqrt{80 t^{5}}}80t5​5t11​​

Simplify by factoring. - 25m21\sqrt{25 m^{21}}25m21​

Add or subtract. Simplify by collecting like radical terms, if possible. - 82−5508 \sqrt{2}-5 \sqrt{50}82​−550​

Divide and simplify. - 6150\frac{\sqrt{6}}{\sqrt{150}}150​6​​

Solve the equation. - x2−3=x+3\sqrt{\mathrm{x}^{2}-3}=\sqrt{\mathrm{x}+3}x2−3​=x+3​

Solve the problem. Give an exact answer and an approximation to the nearest tenth. -A boat travels 4mi4 \mathrm{mi}4mi south and then 6mi6 \mathrm{mi}6mi east. How far is the boat from its starting point? A=4miB=6\mathrm{A}=4 \mathrm{mi} \quad \mathrm{B}=6A=4miB=6

Simplify by factoring. - 175\sqrt{175}175​

Identify the radicand. - 4xy−54 x \sqrt{y-5}4xy−5​

Solve the equation. - x+6+2−x=4\sqrt{\mathrm{x}+6}+\sqrt{2-\mathrm{x}}=4x+6​+2−x​=4