Deck 14: Radical Expressions and Equations

Question 1

Find all square roots of the number.

-441

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

Answer 1

$21,-21$

Question 2

Simplify.

- $\sqrt{16}$

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

Answer 2

4

Question 3

Simplify.

- $-\sqrt{16}$

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

Answer 3

-4

Question 4

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

- $\sqrt{227}$

A) 15.082
B) 15.067
C) 15
D) 15.054

Question 5

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

- $\sqrt{1.93}$

A) 1.404
B) 1.389
C) 1.376
D) 1

Question 6

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

- $\sqrt{0.000103}$

A) 0.1
B) 0.001
C) 1.000
D) 0.010

Question 7

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

- $-\sqrt{0.00127}$

A) -0.004
B) -0.036
C) Not a real number
D) -3.600

Question 8

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

- $\sqrt{\frac{389}{213}}$

A) 2.351
B) 1.251
C) 1.351
D) 1.451

Question 9

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

Question 10

Solve the problem.

-The cost of manufacturing clocks is given by $c=100 \sqrt{n+36}$ , where $c$ is the total cost and $n$ is the number produced. What is $\mathrm{c}$ when no clocks are produced?

A) $\$ 600$
B) $\$ 60$
C) $\$ 3600$
D) $\$ 100$

Question 11

Solve the problem.

-A retailer finds that total costs per day are given by $c=144 \sqrt{n}+81$ , where $c$ is cost and $n$ is units sold. What is $\mathrm{c}$ when no units are sold?

A) $\$ 108$
B) $\$ 1296$
C) $\$ 225$
D) $\$ 81$

Question 12

Identify the radicand.

- $\sqrt{x+3}$

A) $x+3$
B) $\sqrt{ }$
C) $\sqrt{x+3}$
D) $\mathrm{x}$

Question 13

Identify the radicand.

- $\sqrt{y-8}$

A) $y+8$
B) $\sqrt{ }$
C) $\sqrt{y-8}$
D) $y-8$

Question 14

Identify the radicand.

- $2 \sqrt{x^{2}+8}$

A) 2
B) $2 \sqrt{x^{2}+8}$
C) $\sqrt{x^{2}+8}$
D) $x^{2}+8$

Question 15

Identify the radicand.

- $5 x \sqrt{y-8}$

A) y -8
B) $\mathrm{y}$
C) $\sqrt{y-8}$
D) $5 x$

Question 16

Identify the radicand.

- $6 a b \sqrt{b^{2}-3}$

A) $6 \mathrm{ab}$
B) $\sqrt{b^{2}-3}$
C) $b^{2}-3$
D) $b^{2}$

Question 17

Identify the radicand.

- $x y^{2} \sqrt{\frac{9}{x+8}}$

A) $\frac{9}{x+8}$
B) $x y^{2}$
C) $\sqrt{\frac{9}{x+8}}$
D) $x+8$

Question 18

Identify the radicand.

- $s^{2} t \sqrt{\frac{s}{s-3 t}}$

A) $\sqrt{\frac{s}{s-3 t}}$
B) $\frac{s}{s-3 t}$
C) $s^{2} t$
D) $\left(s^{2} t\right) \frac{s}{s-3 t}$

Question 19

Identify the radicand.

- $5 x^{2} y^{2} \sqrt{\frac{4}{5 x-y}}$

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

Question 20

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

- $\sqrt{16}$

Question 21

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

- $-\sqrt{225}$

Question 22

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

- $\sqrt{-(-110)}$

Question 23

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

- $-\sqrt{-136}$

Question 24

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

- $\sqrt{\left(4 x^{2}\right)^{2}}$

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

Question 25

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

- $\sqrt{25 x^{2}}$

A) $-5 x$
B) $25 x$
C) $5 x^{2}$
D) $5 x$

Question 26

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

- $\sqrt{(11 y)^{2}}$

A) $121 \mathrm{y}$
B) $121 \mathrm{y}^{2}$
C) y
D) $11 \mathrm{y}$

Question 27

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

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

A) $5 y-5$
B) $\sqrt{5 y}+\sqrt{|-5|}$
C) $\sqrt{5 y}-\sqrt{|-5|}$
D) $25 y^{2}-50 y+25$

Question 28

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

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

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

Question 29

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) $(5 x+3)^{2}$
C) $5 x+3$
D) $\sqrt{(5 x+3)^{2}}$

Question 30

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

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

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

Question 31

Simplify by factoring.

- $\sqrt{175}$

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

Question 32

Simplify by factoring.

- $\sqrt{375}$

A) $5 \sqrt{15}$
B) $15 \sqrt{5}$
C) 19
D) 75

Question 33

Simplify by factoring.

- $-\sqrt{375}$

A) -75
B) $-5 \sqrt{15}$
C) $-15 \sqrt{5}$
D) -19

Question 34

Simplify by factoring.

- $6 \sqrt{18}$

A) $18 \sqrt{6}$
B) 108
C) 25
D) $18 \sqrt{2}$

Question 35

Simplify by factoring.

- $\sqrt{175 x^{2}}$

A) $5 x \sqrt{7}$
B) $5 \sqrt{7 x}$
C) $7 x^{2} \sqrt{5}$
D) $175 x$

Question 36

Simplify by factoring.

- $\sqrt{128 y^{2}}$

A) $8 \sqrt{2 y^{2}}$
B) $8 y^{2} \sqrt{2}$
C) $8 \sqrt{2}$
D) $8 y \sqrt{2}$

Question 37

Simplify by factoring.

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

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

Question 38

Simplify by factoring.

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

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

Question 39

Simplify by factoring.

- $\sqrt{x^{11}}$

A) $x^{5} \sqrt{x}$
B) $x^{5}$
C) $x^{6}$
D) $x^{4} \sqrt{x}$

Question 40

Simplify by factoring.

- $\sqrt{(x+5)^{18}}$

A) $(x+5)^{9}$
B) $(x+5)^{9} \sqrt{(x+5)}$
C) $x+5^{10}$
D) $(x+5)^{8}$

Question 41

Simplify by factoring.

- $\sqrt{36 m^{7}}$

A) $6 m^{2} \sqrt{m}$
B) $6 \mathrm{~m}^{3}$
C) $6 m^{3} \sqrt{m}$
D) $6 m^{4}$

Question 42

Simplify by factoring.

- $\sqrt{100 m^{19} n^{6}}$

A) $10 m^{9} n^{3}$
B) $10 m^{10} n^{4}$
C) $10 m^{9} n^{3} \sqrt{m}$
D) $10 m^{8} n^{3} \sqrt{m}$

Question 43

Multiply and then, if possible, simplify by factoring.

- $\sqrt{3} \sqrt{6}$

A) $\sqrt{18}$
B) $9 \sqrt{2}$
C) $\sqrt{2}$
D) $3 \sqrt{2}$

Question 44

Multiply and then, if possible, simplify by factoring.

- $\sqrt{26} \sqrt{14}$

A) $\sqrt{364}$
B) $2 \sqrt{91}$
C) $4 \sqrt{91}$
D) $\sqrt{182}$

Question 45

Multiply and then, if possible, simplify by factoring.

- $\sqrt{125} \sqrt{5}$

A) 625
B) 25
C) $5 \sqrt{5}$
D) $5 \sqrt{25}$

Question 46

Multiply and then, if possible, simplify by factoring.

- $\sqrt{10} \sqrt{10 x}$

A) $100 \sqrt{x}$
B) $\sqrt{100} x$
C) $10 x$
D) $10 \sqrt{x}$

Question 47

Multiply and then, if possible, simplify by factoring.

- $\sqrt{3 x} \sqrt{81 y}$

A) $81 \sqrt{x y}$
B) $9 x y$
C) $9 \sqrt{3 x y}$
D) $\sqrt{81 x y}$

Question 48

Multiply and then, if possible, simplify by factoring.

- $\sqrt{5 x} \sqrt{35 x}$

A) $5 x \sqrt{7}$
B) $25 x \sqrt{7}$
C) $5 \sqrt{7 x}$
D) $\sqrt{175 x^{2}}$

Question 49

Multiply and then, if possible, simplify by factoring.

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

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

Question 50

Multiply and then, if possible, simplify by factoring.

- $\sqrt{2 x^{4}} \sqrt{14 x^{6}}$

A) $2 \sqrt{7 x^{10}}$
B) $2 x^{10} \sqrt{7}$
C) $4 x^{5} \sqrt{7}$
D) $2 x^{5} \sqrt{7}$

Question 51

Multiply and then, if possible, simplify by factoring.

- $\sqrt{x^{8} y^{2}} \sqrt{x y^{7}}$

A) $x^{4} y^{4} \sqrt{x y}$
B) $x^{8} y^{8} \sqrt{x y}$
C) $\sqrt{x^{9} y^{9}}$
D) $x^{4} \sqrt{x y^{9}}$

Question 52

Multiply and then, if possible, simplify by factoring.

- $\sqrt{3 x^{2} y} \sqrt{6 x^{7} y^{4}}$

A) $9 x^{8} y^{4} \sqrt{2 x y}$
B) $3 x^{4} y^{2} \sqrt{2}$
C) $3 x^{4} y^{2} \sqrt{2 x y}$
D) $3 \sqrt{2 x^{9} y^{5}}$

Question 53

Multiply and then, if possible, simplify by factoring.

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

A) $\sqrt{21 x-7}$
B) $21 x+49$
C) $\sqrt{21 x-49}$
D) $\sqrt{21 x+49}$

Question 54

Multiply and then, if possible, simplify by factoring.

- $\sqrt{x+8} \sqrt{x+8}$

A) $x^{2}+16 x+64$
B) $\sqrt{x^{2}+64}$
C) $x+8$
D) $\sqrt{x+8}$

Question 55

Divide and simplify.

- $\frac{\sqrt{12}}{\sqrt{3}}$

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

Question 56

Divide and simplify.

- $\frac{\sqrt{4}}{\sqrt{36}}$

A) $3 \sqrt{4}$
B) $\frac{\sqrt{4}}{3}$
C) $\frac{1}{3}$
D) 4

Question 57

Divide and simplify.

- $\frac{\sqrt{32 x}}{\sqrt{2 x}}$

A) 4
B) $4 x$
C) $2 x$
D) 2

Question 58

Divide and simplify.

- $\frac{\sqrt{12 x^{3}}}{\sqrt{3 x}}$

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

Question 59

Simplify.

- $\sqrt{\frac{64}{25}}$

A) $\frac{\sqrt{8}}{\sqrt{5}}$
B) $\frac{\sqrt{8}}{5}$
C) 1
D) $\frac{8}{5}$

Question 60

Simplify.

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

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

Question 61

Simplify.

- $\sqrt{\frac{175 \mathrm{a}^{2}}{\mathrm{c}^{2}}}$

A) $\frac{5 \sqrt{7 a^{2}}}{\text { c }}$
B) $\frac{25 a \sqrt{7}}{\text { c }}$
C) $\frac{5 a \sqrt{7}}{c}$
D) $\frac{a \sqrt{175}}{c}$

Question 62

Simplify.

- $\sqrt{\frac{162 r^{2}}{x^{4}}}$

A) $\frac{9 r \sqrt{2}}{x^{2}}$
B) $\frac{81 \mathrm{r} \sqrt{2}}{\mathrm{x}^{2}}$
C) $\frac{r \sqrt{162}}{x^{2}}$
D) $\frac{9 \sqrt{2 r^{2}}}{x^{2}}$

Question 63

Simplify.

- $\sqrt{\frac{11}{r^{4}}}$

A) $\frac{\sqrt{11}}{r^{2}}$
B) $\frac{\sqrt{11}}{r}$
C) $\frac{\sqrt{11}}{\sqrt{\mathrm{r}^{4}}}$
D) $\frac{\sqrt{11 r^{4}}}{r^{4}}$

Question 64

Simplify.

- $\sqrt{\frac{30}{x^{4} y^{4}}}$

A) $\frac{\sqrt{30}}{x y}$
B) $\frac{\sqrt{30 x^{4} y^{4}}}{x^{4} y^{4}}$
C) $\frac{\sqrt{30}}{x^{2} y^{2}}$
D) $\frac{\sqrt{30}}{x^{4} y^{4}}$

Question 65

Simplify.

- $\frac{\sqrt{2 t^{16}}}{\sqrt{50 t^{6}}}$

A) $\frac{t^{10}}{5}$
B) $\frac{t^{5}}{\sqrt{5}}$
C) $\frac{t^{5}}{5}$
D) $\sqrt{\frac{t^{5}}{5}}$

Question 66

Rationalize the denominator and simplify.

- $\frac{22}{\sqrt{22}}$

A) $22 \sqrt{22}$
B) 22
C) 1
D) $\sqrt{22}$

Question 67

Rationalize the denominator and simplify.

- $\frac{16 \sqrt{13}}{28 \sqrt{7}}$

A) $\frac{4 \sqrt{91}}{7}$
B) $\frac{4 \sqrt{91}}{49}$
C) $\frac{4 \sqrt{13}}{49}$
D) $\frac{4 \sqrt{13}}{7}$

Question 68

Rationalize the denominator and simplify.

- $\frac{3}{\sqrt{23}}$

A) $\frac{9 \sqrt{23}}{23}$
B) 532
C) $3 \sqrt{23}$
D) $\frac{3 \sqrt{23}}{23}$

Question 69

Rationalize the denominator and simplify.

- $\sqrt{\frac{25}{28}}$

A) 28
B) $\frac{5 \sqrt{7}}{14}$
C) $5 \sqrt{7}$
D) $\frac{5 \sqrt{7}}{7}$

Question 70

Rationalize the denominator and simplify.

- $\frac{7 x}{\sqrt{3}}$

A) $7 x \sqrt{3}$
B) $\frac{7 x \sqrt{3}}{3}$
C) 16
D) $\frac{49 x \sqrt{3}}{3}$

Question 71

Rationalize the denominator and simplify.

- $\frac{2}{\sqrt{17}}$

A) 291
B) $2 \sqrt{17}$
C) $\frac{2 \sqrt{17}}{17}$
D) $\frac{4 \sqrt{17}}{17}$

Question 72

Rationalize the denominator and simplify.

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

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

Question 73

Rationalize the denominator and simplify.

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

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

Question 74

Rationalize the denominator and simplify.

- $\frac{\sqrt{x^{11}}}{\sqrt{\mathrm{xy}^{4}}}$

A) $\frac{x^{6}}{x y^{2}}$
B) $\frac{x^{5}}{y^{2}}$
C) $\frac{x^{5}}{y^{3}}$
D) $\frac{x^{6}}{y^{2}}$

Question 75

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

- $-14 \sqrt{3}+5 \sqrt{3}$

A) $-9 \sqrt{3}$
B) $20 \sqrt{3}$
C) $8 \sqrt{3}$
D) $-19 \sqrt{3}$

Question 76

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

- $30 \sqrt{11}-12 \sqrt{11}$

A) $42 \sqrt{11}$
B) 198
C) 18
D) $18 \sqrt{11}$

Question 77

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

- $2 \sqrt{6}+9 \sqrt{54}$

A) $29 \sqrt{6}$
B) $25 \sqrt{6}$
C) $-29 \sqrt{6}$
D) $11 \sqrt{6}$

Question 78

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

- $7 \sqrt{98}-7 \sqrt{200}$

A) $21 \sqrt{2}$
B) $-21 \sqrt{2}$
C) $119 \sqrt{2}$
D) $-119 \sqrt{2}$

Question 79

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

- $-2 \sqrt{48}-4 \sqrt{192}+3 \sqrt{108}$

A) $-2 \sqrt{3}$
B) $-138 \sqrt{3}$
C) $-22 \sqrt{3}$
D) $138 \sqrt{3}$

Question 80

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

- $\sqrt{128}+9 \sqrt{32}+5 \sqrt{98}$

A) $79 \sqrt{2}$
B) $-32 \sqrt{2}$
C) $-79 \sqrt{2}$
D) $-4 \sqrt{2}$