﻿ Solving Square Root Functions Worksheet | Problems & Solutions

# Solving Square Root Functions Worksheet

Solving Square Root Functions Worksheet
• Page 1
1.
Simplify:
$\sqrt{192}$

 a. 5$\sqrt{3}$ b. 2$\sqrt{5}$ c. 3$\sqrt{7}$ d. 8$\sqrt{3}$

#### Solution:

192
[ Original expression.]

= (64×3)
[Factor 192 as 64 × 3.]

= (3×(82))

= 83

2.
Simplify:
$\sqrt{162}$

 a. 3$\sqrt{2}$ b. 5$\sqrt{6}$ c. 9$\sqrt{2}$ d. 2$\sqrt{3}$

#### Solution:

162
[ Original expression.]

= (81×2)
[Factor 162 as 81 × 2.]

= (2×(92))

92

3.
Simplify:
$\sqrt{48}$

 a. 4$\sqrt{3}$ b. 3$\sqrt{2}$ c. 2$\sqrt{3}$ d. 3$\sqrt{4}$

#### Solution:

48
[ Original expression.]

= (16×3)
[Factor 48 as 16 × 3.]

= (3×(42))

= 43

4.
Simplify:
$\sqrt{72}$

 a. 3$\sqrt{6}$ b. 5$\sqrt{3}$ c. 2$\sqrt{6}$ d. 6$\sqrt{2}$

#### Solution:

72
[Original expression.]

= (36×2)
[Factor 72 as 36 × 2.]

= (2×(62))

= 62

5.
Simplify:
$\sqrt{28}$
 a. 2$\sqrt{7}$ b. 3$\sqrt{7}$ c. 7$\sqrt{3}$ d. 3$\sqrt{2}$

#### Solution:

28
[Original expression.]

=7 × 4
[Factor 28 as 7 × 4.]

=7×(22)

=27

6.
Find the domain and the range of $y$ = $x$$\sqrt{8x}$.
 a. Both domain and range are all negative real numbers. b. Both domain and range are all non-negative real numbers. c. Domain: all real numbers greater than or equal to 8; range: all non-negative real numbers. d. Domain: all non-negative real numbers; range: all real numbers greater than or equal to 8.

#### Solution:

Find the values of x for which the function is defined.

The function x8x exists only for 8x ≥ 0 x ≥ 0.

The domain is the set of all non-negative real numbers.

The range of the function is the set of all non-negative real numbers.

7.
Which of the following functions best represents the graph?

 a. $y$ = $\sqrt{x}$ + 7 b. $y$ = c. $y$ = $\sqrt{2x}$ + 1 d. $y$ =

#### Solution:

On the graph, (2, 3) and (- 3, 2) points are marked. So, the function representing the graph should satisfy these two points.

Consider the function y = x + 7, if x = 2 then y = 8.414. So, this is not the required function.

Consider the function y = 2x + 5, if x = 2, then y = 3 and when x = - 3, then y is undefined. So, this is not the required function.

Consider the function y = 2x + 1, if x = 2, then y = 3 and when x = - 3, then y is undefined. So, this is not the required function.

Consider the function y = x + 7, if x = 2, then y = 3 and when x = - 3, then y = 2. So, this is the required function.

8.
Which of the following functions best represents the graph?

 a. b. c. d. $\sqrt{4x}$ - 1

#### Solution:

The two points on the graph (1, - 1) and (4, 0) satisfy the funciton x - 2x.

9.
The period T in seconds and the length L in inches of the pendulum are related as T = 2$\pi$$\sqrt{\frac{L}{384}}$. Find the length of the pendulum in inches with period of 6 seconds.
 a. 350.17 b. 102.76 c. 580.64 d. 298.32

#### Solution:

T = 2πL384

T2 = (2π)2L384
[Square on both sides.]

384 · T2 = (2π)2L
[Multiply both sides with 384.]

L = T2384(2π)2
[Divide both sides by (2π )2.]

L = (6)2384(2π)2
[Substitute 6 for T.]

L = 350.17 inches.

The length of the pendulum = 350.17 inches.

10.
Find the lateral surface area $s$ of a cone whose base radius $r$ is 3 cm and height $h$ is 4 cm.
Use the formula $s$ = $\pi$ $r$ .
 a. 5$\pi$ sq.cm. b. 15$\pi$ sq.cm. c. 8$\pi$ sq.cm. d. 24$\pi$ sq.cm.

#### Solution:

s = π r r2 +h2

= 3π 9 + 16
[Replace r with 3 and h with 4.]

= 15π sq.cm.