Deck 10: Radical Expressions, Equations, and Functions

Question 1

Find the square roots.
2500

A) $51 , - 51$
B) $52 , - 52$
C) $50 , - 50$
D) $100 , - 100$

Answer 1

C

Question 2

Use a calculator to approximate to three decimal places.
$$\sqrt { \frac { 449.7 } { 89.7 } }$$

A) $1902.190$
B) $5.013$
C) $0.239$
D) $2.239$

Answer 2

D

Question 3

Simplify.
$$- \sqrt { \frac { 361 } { 81 } }$$

A) $- \frac { 180 } { 40 }$
B) $\frac { 19 } { 9 }$
C) does not exist as a real number
D) $- \frac { 19 } { 9 }$

Answer 3

D

Question 4

Use a calculator to approximate to three decimal places.
$- \sqrt { 926 }$

A) $- 30.430$
B) $- 30.417$
C) $30.445$
D) 30

Question 5

Simplify.
$- \sqrt { 0.25 }$

A) does not exist as a real number
B) $0.05$
C) $- 0.05$
D) $- 0.5$

Question 6

Use a calculator to approximate to three decimal places.
$\sqrt { 0.000227 }$

A) $0.015$
B) $0.15$
C) $0.002$
D) $1.500$

Question 7

Use a calculator to approximate to three decimal places.
$\sqrt { \frac { 326 } { 67 } }$

A) $1209.716$
B) $2.206$
C) $4.866$
D) $0.206$

Question 8

Simplify.
$$\sqrt { \frac { 400 } { 289 } }$$

A) $\frac { 10 } { 9 }$
B) $\frac { 25 } { 18 }$
C) $\frac { 21 } { 17 }$
D) $\frac { 20 } { 17 }$

Question 9

Simplify.
$\sqrt { 0.09 }$

A) $0.003$
B) $0.3$
C) $0.03$
D) 3

Question 10

Use a calculator to approximate to three decimal places.
$\sqrt { 0.00109 }$

A) $3.300$
B) $0.033$
C) $0.003$
D) $0.33$

Question 11

Simplify.
$\sqrt { 529 }$

A) 24
B) does not exist as a real number
C) 23
D) 264

Question 12

Simplify.
$\sqrt { - 144 }$

A) 13
B) 72
C) 12
D) does not exist as a real number

Question 13

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

A) $\sqrt { }$
B) $y - 5$
C) $\sqrt { y - 5 }$
D) $y + 5$

Question 14

Use a calculator to approximate to three decimal places.
$\sqrt { 2.27 }$

A) 1
B) $1.507$
C) $1.522$
D) $1.494$

Question 15

Identify the radicand.
$$\sqrt { x + 9 }$$

A) $\sqrt { x + 9 }$
B) $x + 9$
C) $x$
D) $\sqrt { }$

Question 16

Find the square roots.
324

A) $19 , - 19$
B) $36 , - 36$
C) $20 , - 20$
D) $18 , - 18$

Question 17

Simplify.
$- \sqrt { 256 }$

A) $- 16$
B) does not exist as a real number
C) 16
D) $- 128$

Question 18

Identify the radicand.
$9 x \sqrt { y - 4 }$

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

Question 19

Use a calculator to approximate to three decimal places.
$\sqrt { 197 }$

A) $14.023$
B) $14.051$
C) 14
D) $14.036$

Question 20

Identify the radicand.
$2 \sqrt { \mathrm { x } ^ { 2 } + 5 }$

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

Question 21

For the given function, find the indicated function value.
For $g ( x ) = \sqrt { x ^ { 2 } - 20 }$ , find $g ( 7 )$ .

A) $2 \sqrt { 30 }$
B) $\sqrt { 30 }$
C) $3 \sqrt { 29 }$
D) $\sqrt { 29 }$

Question 22

Find the domain of f.
$$f ( x ) = \sqrt { 11 - 4 x }$$

A) $\left\{ x \mid x \leq \frac { 11 } { 4 } \right\}$
B) $\left\{ x \mid x \geq - \frac { 11 } { 4 } \right\}$
C) $\left\{ x \mid x \geq \frac { 11 } { 4 } \right\}$
D) $\left\{ x \mid x < \frac { 11 } { 4 } \right\}$

Question 23

For the given function, find the indicated function value.
For $g ( x ) = - \sqrt { ( x + 1 ) ^ { 2 } }$ , find $g ( - 10 )$

A) 10
B) $- 9$
C) $- 10$
D) 9

Question 24

Find the domain of f.
$$f ( x ) = \sqrt { x + 19 }$$

A) $\{ x \mid x < - 19 \}$
B) $\{ x \mid x \geq - 19 \}$
C) $\{ x \mid x < 19 \}$
D) $\{ x \mid x \geq 19 \}$

Question 25

Graph.
$f(x)=\sqrt{x+3}$

A)

B)

C)

D)

Question 26

For the given function, find the indicated function value.
For $f ( x ) = \sqrt { 4 x - 14 }$ , find $f ( - 6 )$

A) Does not exist as a real number
B) $\sqrt { 15 }$
C) $3 \sqrt { 13 }$
D) $2 \sqrt { 7 }$

Question 27

Identify the radicand.
$8 a b \sqrt { b ^ { 2 } - 6 }$

A) $8 \mathrm { ab }$
B) $\sqrt { b ^ { 2 } - 6 }$
C) $b ^ { 2 }$
D) $b ^ { 2 } - 6$

Question 28

Answer the question.
The cost of manufacturing clocks is given by $\mathrm { c } = 49 \sqrt { \mathrm { n } + 16 }$ , where $\mathrm { c }$ is the total cost and $\mathrm { n }$ is the number produced. What is c when no clocks are produced?

A) $\$ 784$
B) $\$ 196$
C) $\$ 49$
D) $\$ 28$

Question 29

Graph.
$f(x)=-\sqrt{8-x}$

A)

B)

C)

D)

Question 30

Graph.
$$g ( x ) = - 2 \sqrt { x }$$

A)

B)

C)

D)

Question 31

Identify the radicand.
$$2 x ^ { 2 } y ^ { 2 } \sqrt { \frac { 5 } { 6 x - y } }$$

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

Question 32

Answer the question.
A retailer finds that total costs per day are given by $c = 16 \sqrt { n } + 169$ , where $c$ is cost and $n$ is units sold. What is $c$ when no units are sold?

A) $\$ 169$
B) $\$ 52$
C) $\$ 208$
D) $\$ 185$

Question 33

Identify the radicand.
$x y ^ { 2 } \sqrt { \frac { 4 } { x + 6 } }$

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

Question 34

For the given function, find the indicated function value.
For $g ( x ) = \sqrt { ( x - 1 ) ^ { 2 } }$ , find $g ( 3 )$ .

A) 4
B) 3
C) 2
D) 1

Question 35

Answer the question.
Police use a formula $s = S \sqrt { \frac { l } { L } }$ , where $S$ is the test-car speed and $L$ is the test-skid length, to find the actual speed $s$ in an accident which left a skid mark of l. Find the speed (nearest whole mph) when $S = 54 \mathrm { mph }$ , $l = 150 \mathrm { ft } , \mathrm { L } = 100 \mathrm { ft }$ .

A) $66 \mathrm { mph }$
B) $44 \mathrm { mph }$
C) $81 \mathrm { mph }$
D) $104 \mathrm { mph }$

Question 36

For the given function, find the indicated function value.
For $g ( x ) = \sqrt { x ^ { 2 } - 20 }$ , find $g ( 3 )$ .

A) $3 \sqrt { 5 }$
B) $2 \sqrt { 3 }$
C) $\sqrt { 7 }$
D) Does not exist as a real number

Question 37

For the given function, find the indicated function value.
For $f ( x ) = \sqrt { 4 x - 14 }$ , find $f ( 14 )$ .

A) $\sqrt { 43 }$
В) $\sqrt { 41 }$
C) $2 \sqrt { 41 }$
D) $\sqrt { 42 }$

Question 38

Identify the radicand.
$s ^ { 2 } t \sqrt { \frac { s } { s - 8 t } }$

A) $\sqrt { \frac { s } { s - 8 t } }$
B) $\left( s ^ { 2 } t \right) \frac { s } { s - 8 t }$
C) $\frac { s } { s - 8 t }$
D) $\mathrm { s } ^ { 2 } \mathrm { t }$

Question 39

Find the domain of f.
$$f ( x ) = \sqrt { x - 17 }$$

A) $\{ x \mid x \geq 0 \}$
B) $\{ x \mid x \geq 17 \}$
C) All real numbers
D) $\{ x \mid x \geq - 17 \}$

Question 40

Find the domain of f.
$$f ( x ) = \sqrt { 9 x + 4 }$$

A) $\left\{ x \mid x \leq - \frac { 4 } { 9 } \right\}$
B) $\left\{ x \mid x \geq \frac { 4 } { 9 } \right\}$
C) $\left\{ x \mid x > - \frac { 4 } { 9 } \right\}$
D) $\left\{ x \mid x \geq - \frac { 4 } { 9 } \right\}$

Question 41

Graph.
$$g ( x ) = 3 + \sqrt { x - 1 }$$

A)

B)

C)

D)

Question 42

Graph.
$$g ( x ) = \sqrt { 4 - 8 x }$$

A)

B)

C)

D)

Question 43

Find the following. Assume that the letter can represent any real number.
$\sqrt { \mathrm { x } ^ { 2 } }$

A) $| x |$
B) $x$
C) $- | x |$
D) $\left| x ^ { 2 } \right|$

Question 44

Find the following. Assume that the letter can represent any real number.
$\sqrt { 9 x ^ { 2 } }$

A) $9 x$
B) $- 3 | x |$
C) $3 | x |$
D) $3 x$

Question 45

Graph.
$g(x)=\sqrt{3 x+3}$

A)

B)

C)

D)

Question 46

Graph.
$$g ( x ) = 4 + \sqrt { x }$$

A)

B)

C)

D)