Deck 8: Radical Expressions and Equations

Question 1

Find all square roots of the number.

-441

A) $21,-21$
B) $23,-23$
C) $22,-22$
D) $42,-42$

Answer 1

$21,-21$

Question 2

Simplify.

- $\sqrt{49}$

A) 8
B) 7
C) 24
D) Not a real number

Answer 2

7

Question 3

Simplify.

- $-\sqrt{16}$

A) -4
B) Not a real number
C) -8
D) - 5

Answer 3

-4

Question 4

Simplify.

- $\sqrt{225}$

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

Question 5

Use a calculator to approximate the square root. Round to three decimal places.

- $\sqrt{107}$

A) 10
B) 10.359
C) 10.344
D) 10.331

Question 6

Use a calculator to approximate the square root. Round to three decimal places.

- $\sqrt{1.03}$

A) 1.030
B) 1.002
C) 1
D) 1.015

Question 7

Use a calculator to approximate the square root. Round to three decimal places.

- $\sqrt{0.000191}$

A) 0.014
B) 0.14
C) 1.400
D) 0.001

Question 8

Use a calculator to approximate the square root. Round to three decimal places.

- $-\sqrt{0.00139}$

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

Question 9

Use a calculator to approximate the square root. Round to three decimal places.

- $\sqrt{\frac{112}{95}}$

A) 1.086
B) 0.986
C) 1.186
D) 2.086

Question 10

Solve the problem.

-The distance in miles that can be seen on the surface of the ocean is given by $d=1.4 \sqrt{h}$ where $h$ is the height above the surface of the water. How many feet high above the water (to the nearest tenth) would a pirate have to climb to see 17 miles?

A) $73.7 \mathrm{ft}$
B) $147.4 \mathrm{ft}$
C) $566.4 \mathrm{ft}$
D) $5.8 \mathrm{ft}$

Question 11

Solve the problem.

-The cost of manufacturing clocks is given by $c=81 \sqrt{n+49}$ , where $c$ is the total cost and $n$ is the number produced. What is $\mathrm{c}$ when no clocks are produced?

A) $\$ 81$
B) $\$ 63$
C) $\$ 567$
D) $\$ 3969$

Question 12

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?

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

Question 13

Identify the radicand.

- $\sqrt{\mathrm{x}+5}$

A) $\mathrm{x}$
B) $\sqrt{ }$
C) $\sqrt{\mathrm{x}+5}$
D) $\mathrm{x}+5$

Question 14

Identify the radicand.

- $\sqrt{\mathrm{y}-7}$

A) $\mathrm{y}-7$
B) $\sqrt{ }$
C) $\sqrt{y-7}$
D) $y+7$

Question 15

Identify the radicand.

- $6 \sqrt{x^{2}+2}$

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

Question 16

Identify the radicand.

- $4 x \sqrt{y-5}$

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

Question 17

Identify the radicand.

- $4 \mathrm{ab} \sqrt{\mathrm{b}^{2}-9}$

A) $b^{2}$
B) $\sqrt{b^{2}-9}$
C) $b^{2}-9$
D) $4 \mathrm{ab}$

Question 18

Identify the radicand.

- $x y^{2} \sqrt{\frac{5}{x+6}}$

A) $x y^{2}$
B) $x+6$
C) $\frac{5}{x+6}$
D) $\sqrt{\frac{5}{x+6}}$

Question 19

Identify the radicand.

- $s^{2} t \sqrt{\frac{s}{s-5 t}}$

A) $\sqrt{\frac{s}{s-5 t}}$
B) $\frac{s}{s-5 t}$
C) $\left(s^{2} t\right) \frac{s}{s-5 t}$
D) $s^{2} t$

Question 20

Identify the radicand.

- $6 x^{2} y^{2} \sqrt{\frac{2}{5 x-y}}$

A) $5 x-y$
B) $6 x^{2} y^{2}$
C) $\sqrt{\frac{2}{5 x-y}}$
D) $\frac{2}{5 x-y}$

Question 21

Decide whether or not the radical expression represents a real number.

- $\sqrt{16}$

Question 22

Decide whether or not the radical expression represents a real number.

- $-\sqrt{100}$

Question 23

Decide whether or not the radical expression represents a real number.

- $\sqrt{-(-107)}$

Question 24

Decide whether or not the radical expression represents a real number.

- $-\sqrt{-140}$

Question 25

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number.

- $\sqrt{\left(9 x^{2}\right)^{2}}$

A) $3 x^{2}$
B) $9 \mathrm{x}$
C) $3 \mathrm{x}$
D) $9 x^{2}$

Question 26

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number.

- $\sqrt{49 x^{2}}$

A) $49 x$
B) $7 x^{2}$
C) $7 \mathrm{x}$
D) $-7 \mathrm{x}$

Question 27

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number.

- $\sqrt{(15 y)^{2}}$

A) $225 y^{2}$
B) $\mathrm{y}$
C) $225 y$
D) $15 y$

Question 28

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number.

- $\sqrt{(3 y+5)^{2}}$

A) $\sqrt{3 y}+\sqrt{|5|}$
B) $3 y+5$
C) $9 y^{2}+30 y+25$
D) $\sqrt{3 y}-\sqrt{|5|}$

Question 29

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number.

- $\sqrt{z^{2}-10 z+25}$

A) $\sqrt{z}-\sqrt{|-5|}$
B) $(z-5)^{2}$
C) $\sqrt{z}+\sqrt{|-5|}$
D) $\mathrm{z}-5$

Question 30

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number.

- $\sqrt{25 x^{2}+30 x+9}$

A) none of these
B) $(5 \mathrm{x}+3)^{2}$
C) $5 x+3$
D) $\sqrt{(5 x+3)^{2}}$

Question 31

Simplify. Remember that we have assumed that radicands do not represent the square of a negative number.

- $\sqrt{(z-2)^{2}}$

A) $\mathrm{z}-2$
B) $\sqrt{\mathrm{z}}-2$
C) $(\mathrm{z}-2)^{2}$
D) $\mathrm{z}-\sqrt{2}$

Question 32

Simplify by factoring.

- $\sqrt{175}$

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

Question 33

Simplify by factoring.

- $\sqrt{490}$

A) $7 \sqrt{10}$
B) 70
C) $10 \sqrt{7}$
D) 22

Question 34

Simplify by factoring.

- $-\sqrt{432}$

A) -20
B) -72
C) $-12 \sqrt{6}$
D) $-12 \sqrt{3}$

Question 35

Simplify by factoring.

- $2 \sqrt{21}$

A) 42
B) 9
C) $21 \sqrt{2}$
D) $2 \sqrt{21}$

Question 36

Simplify by factoring.

- $\sqrt{150 x^{2} y}$

A) $5 x^{2} \sqrt{6 y}$
B) $5 x y \sqrt{6}$
C) $5 x y^{2} \sqrt{6}$
D) $5 x \sqrt{6 y}$

Question 37

Simplify by factoring.

- $\sqrt{75 x^{2}}$

A) $75 x$
B) $5 \sqrt{3 x}$
C) $5 x \sqrt{3}$
D) $3 x^{2} \sqrt{5}$

Question 38

Simplify by factoring.

- $\sqrt{486 y^{2}}$

A) $9 y \sqrt{6}$
B) $9 \sqrt{6 y^{2}}$
C) $9 \sqrt{6}$
D) $9 y^{2} \sqrt{6}$

Question 39

Simplify by factoring.

- $\sqrt{25 z+10 z^{2}+z^{3}}$

A) $\sqrt{z}+\sqrt{|5|}$
B) $\sqrt{\mathrm{z}}(\mathrm{z}+5)$
C) $(z+5)^{2}$
D) $z+5$

Question 40

Simplify by factoring.

- $\sqrt{\mathrm{x}^{6}}$

A) $x^{4}$
B) $x^{3} \sqrt{x}$
C) $x^{2}$
D) $x^{3}$

Question 41

Simplify by factoring.

- $\sqrt{x^{13}}$

A) $x^{6} \sqrt{x}$
B) $x^{5} \sqrt{x}$
C) $x^{6}$
D) $x^{7}$

Question 42

Simplify by factoring.

- $\sqrt{(x-5)^{16}}$

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

Question 43

Simplify by factoring.

- $\sqrt{25 m^{21}}$

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 44

Simplify by factoring.

- $\sqrt{9 m^{15} n^{4}}$

A) $3 m^{7} n^{2}$
B) $3 m^{8} n^{3}$
C) $3 m^{6} n^{2} \sqrt{m}$
D) $3 m^{7} n^{2} \sqrt{m}$

Question 45

Multiply and then, if possible, simplify by factoring.

- $\sqrt{3} \sqrt{15}$

A) $9 \sqrt{5}$
B) $\sqrt{45}$
C) $\sqrt{5}$
D) $3 \sqrt{5}$

Question 46

Multiply and then, if possible, simplify by factoring.

- $\sqrt{10} \sqrt{14}$

A) $\sqrt{70}$
B) $\sqrt{140}$
C) $2 \sqrt{35}$
D) $4 \sqrt{35}$

Question 47

Multiply and then, if possible, simplify by factoring.

- $\sqrt{64} \sqrt{4}$

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

Question 48

Multiply and then, if possible, simplify by factoring.

- $\sqrt{7} \sqrt{7 x}$

A) $\sqrt{49} x$
B) $7 \mathrm{x}$
C) $7 \sqrt{\mathrm{x}}$
D) $49 \sqrt{\mathrm{x}}$

Question 49

Multiply and then, if possible, simplify by factoring.

- $\sqrt{7 x} \sqrt{2401 y}$

A) $49 x y$
B) $\sqrt{2401 x y}$
C) $2401 \sqrt{x y}$
D) $49 \sqrt{7 \mathrm{xy}}$

Question 50

Multiply and then, if possible, simplify by factoring.

- $\sqrt{5 x} \sqrt{15 x}$

A) $5 x \sqrt{3}$
B) $5 \sqrt{3 x}$
C) $25 x \sqrt{3}$
D) $\sqrt{75 x^{2}}$

Question 51

Multiply and then, if possible, simplify by factoring.

- $\sqrt{\mathrm{rs}} \sqrt{\mathrm{st}}$

A) $s \sqrt{\mathrm{rt}}$
B) $\sqrt{\mathrm{rst}}$
C) $s^{2} \sqrt{\mathrm{rt}}$
D) $\sqrt{r s^{2} t}$

Question 52

Multiply and then, if possible, simplify by factoring.

- $\sqrt{2 x^{2}} \sqrt{22 x^{4}}$

A) $2 \sqrt{11 x^{6}}$
B) $2 x^{3} \sqrt{11}$
C) $4 x^{3} \sqrt{11}$
D) $2 x^{6} \sqrt{11}$

Question 53

Multiply and then, if possible, simplify by factoring.

- $\sqrt{x^{4} y^{2}} \sqrt{x y^{9}}$

A) $x^{4} y 10 \sqrt{x y}$
B) $\sqrt{x^{5} y^{11}}$
C) $x^{2} y^{5} \sqrt{x y}$
D) $x^{2} \sqrt{x y^{11}}$

Question 54

Multiply and then, if possible, simplify by factoring.

- $\sqrt{2 x^{2} y} \sqrt{6 x^{5} y^{6}}$

A) $2 x^{3} y^{3} \sqrt{3}$
B) $2 \sqrt{3 x^{7} y^{7}}$
C) $2 x^{3} y^{3} \sqrt{3 x y}$
D) $4 x^{6} y^{6} \sqrt{3 x y}$

Question 55

Multiply and then, if possible, simplify by factoring.

- $\sqrt{7} \sqrt{3 \mathrm{x}+1}$

A) $21 \mathrm{x}-7$
B) $\sqrt{21 \mathrm{x}-7}$
C) $\sqrt{21 x+7}$
D) $\sqrt{21 x+1}$

Question 56

Multiply and then, if possible, simplify by factoring.

- $\sqrt{\mathrm{x}-3} \sqrt{\mathrm{x}-3}$

A) $\sqrt{x^{2}+9}$
B) $\sqrt{\mathrm{x}-3}$
C) $x^{2}-6 x+9$
D) $x-3$

Question 57

Divide and simplify.

- $\frac{\sqrt{20}}{\sqrt{5}}$

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

Question 58

Divide and simplify.

- $\frac{\sqrt{6}}{\sqrt{150}}$

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

Question 59

Divide and simplify.

- $\frac{\sqrt{16 x}}{\sqrt{4 x}}$

A) 4
B) $2 \mathrm{x}$
C) 2
D) $4 \mathrm{x}$

Question 60

Divide and simplify.

- $\frac{\sqrt{180 x^{3}}}{\sqrt{5 x}}$

A) $5 \mathrm{x}$
B) $6 x$
C) $6 x^{2}$
D) 5

Question 61

Simplify.

- $\sqrt{\frac{100}{49}}$

A) $\frac{\sqrt{10}}{\sqrt{7}}$
B) $\frac{\sqrt{10}}{7}$
C) $\frac{10}{7}$
D) 1

Question 62

Simplify.

- $\sqrt{\frac{27 \mathrm{x}^{2}}{25}}$

A) $x \sqrt{\frac{27}{5}}$
B) $\frac{3 \sqrt{3 x^{2}}}{5}$
C) $\frac{3 x \sqrt{3}}{5}$
D) $9 x \sqrt{3}$

Question 63

Simplify.

- $\sqrt{\frac{54 \mathrm{a}^{2}}{\mathrm{c}^{2}}}$

A) $\frac{3 a \sqrt{6}}{c}$
B) $\frac{3 \sqrt{6 a^{2}}}{\mathrm{c}}$
C) $\frac{9 \mathrm{a} \sqrt{6}}{\mathrm{c}}$
D) $\frac{\mathrm{a} \sqrt{54}}{\mathrm{C}}$

Question 64

Simplify.

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

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 65

Simplify.

- $\sqrt{\frac{14}{\mathrm{r}^{4}}}$

A) $\frac{\sqrt{14 r^{4}}}{r^{4}}$
B) $\frac{\sqrt{14}}{r}$
C) $\frac{\sqrt{14}}{\sqrt{\mathrm{r}^{4}}}$
D) $\frac{\sqrt{14}}{r^{2}}$

Question 66

Simplify.

- $\sqrt{\frac{19}{\mathrm{x}^{4} \mathrm{y}^{4}}}$

A) $\frac{\sqrt{19}}{x^{2} y^{2}}$
B) $\frac{\sqrt{19 x^{4} y^{4}}}{x^{4} y^{4}}$
C) $\frac{\sqrt{19}}{x^{4} y^{4}}$
D) $\frac{\sqrt{19}}{x y}$

Question 67

Simplify.

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

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

Question 68

Rationalize the denominator and simplify.

- $\frac{6}{\sqrt{6}}$

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

Question 69

Rationalize the denominator and simplify.

- $\frac{4 \sqrt{13}}{6 \sqrt{3}}$

A) $\frac{2 \sqrt{39}}{3}$
B) $\frac{2 \sqrt{13}}{3}$
C) $\frac{2 \sqrt{13}}{9}$
D) $\frac{2 \sqrt{39}}{9}$

Question 70

Rationalize the denominator and simplify.

- $\sqrt{\frac{36}{5}}$

A) 31
B) $6 \sqrt{5}$
C) $\frac{6 \sqrt{5}}{5}$
D) $\frac{36 \sqrt{5}}{5}$

Question 71

Rationalize the denominator and simplify.

- $\frac{9}{\sqrt{14}}$

A) $9 \sqrt{14}$
B) $\frac{9 \sqrt{14}}{14}$
C) 205
D) $\frac{81 \sqrt{14}}{14}$

Question 72

Rationalize the denominator and simplify.

- $\sqrt{\frac{9}{40}}$

A) $3 \sqrt{10}$
B) $\frac{3 \sqrt{10}}{20}$
C) $\frac{3 \sqrt{10}}{10}$
D) 40

Question 73

Rationalize the denominator and simplify.

- $\frac{5 x}{\sqrt{3}}$

A) $\frac{5 x \sqrt{3}}{3}$
B) 14
C) $\frac{25 x \sqrt{3}}{3}$
D) $5 x \sqrt{3}$

Question 74

Rationalize the denominator and simplify.

- $\frac{3}{\sqrt{10}}$

A) $\frac{3 \sqrt{10}}{10}$
B) $3 \sqrt{10}$
C) 103
D) $\frac{9 \sqrt{10}}{10}$

Question 75

Rationalize the denominator and simplify.

- $\sqrt{\frac{98}{\mathrm{x}}}$

A) $\frac{7 \sqrt{2 x}}{x}$
B) $\frac{\sqrt{7 x}}{x}$
C) $7 \sqrt{2 x}$
D) $7 \sqrt{\frac{2}{\mathrm{x}}}$

Question 76

Rationalize the denominator and simplify.

- $\sqrt{\frac{45 x^{3}}{y^{5}}}$

A) $\frac{3 x \sqrt{5 x y}}{y^{3}}$
B) $\frac{3 x^{3} \sqrt{5}}{y^{5}}$
C) $\frac{x \sqrt{45 x y}}{y^{3}}$
D) $\frac{3 x}{y^{2}} \sqrt{\frac{5 x}{y}}$

Question 77

Rationalize the denominator and simplify.

- $\frac{\sqrt{\mathrm{x}^{5}}}{\sqrt{\mathrm{xy}^{8}}}$

A) $\frac{x^{2}}{y^{5}}$
B) $\frac{x^{2}}{y^{4}}$
C) $\frac{x^{3}}{y^{4}}$
D) $\frac{x^{3}}{x y^{4}}$

Question 78

Add or subtract. Simplify by collecting like radical terms, if possible.

- $-4 \sqrt{7}-3 \sqrt{7}$

A) $-1 \sqrt{7}$
B) $-7 \sqrt{7}$
C) $6 \sqrt{7}$
D) $2 \sqrt{7}$

Question 79

Add or subtract. Simplify by collecting like radical terms, if possible.

- $20 \sqrt{5}-13 \sqrt{5}$

A) $33 \sqrt{5}$
B) 7
C) 35
D) $7 \sqrt{5}$

Question 80

Add or subtract. Simplify by collecting like radical terms, if possible.

- $8 \sqrt{2}-5 \sqrt{50}$

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