Solving Square Root Functions Worksheet

**Page 1**

1.

Simplify:

$\sqrt{192}$

$\sqrt{192}$

a. | 5$\sqrt{3}$ | ||

b. | 2$\sqrt{5}$ | ||

c. | 3$\sqrt{7}$ | ||

d. | 8$\sqrt{3}$ |

[ Original expression.]

=

[Factor 192 as 64 × 3.]

=

= 8

Correct answer : (4)

2.

Simplify:

$\sqrt{162}$

$\sqrt{162}$

a. | 3$\sqrt{2}$ | ||

b. | 5$\sqrt{6}$ | ||

c. | 9$\sqrt{2}$ | ||

d. | 2$\sqrt{3}$ |

[ Original expression.]

=

[Factor 162 as 81 × 2.]

=

9

Correct answer : (3)

3.

Simplify:

$\sqrt{48}$

$\sqrt{48}$

a. | 4$\sqrt{3}$ | ||

b. | 3$\sqrt{2}$ | ||

c. | 2$\sqrt{3}$ | ||

d. | 3$\sqrt{4}$ |

[ Original expression.]

=

[Factor 48 as 16 × 3.]

=

= 4

Correct answer : (1)

4.

Simplify:

$\sqrt{72}$

$\sqrt{72}$

a. | 3$\sqrt{6}$ | ||

b. | 5$\sqrt{3}$ | ||

c. | 2$\sqrt{6}$ | ||

d. | 6$\sqrt{2}$ |

[Original expression.]

=

[Factor 72 as 36 × 2.]

=

= 6

Correct answer : (4)

5.

Simplify:

$\sqrt{28}$

$\sqrt{28}$

a. | 2$\sqrt{7}$ | ||

b. | 3$\sqrt{7}$ | ||

c. | 7$\sqrt{3}$ | ||

d. | 3$\sqrt{2}$ |

[Original expression.]

=

[Factor 28 as 7 × 4.]

=

=2

Correct answer : (1)

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. |

The function

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.

Correct answer : (2)

7.

Which of the following functions best represents the graph?

a. | $y$ = $\sqrt{x}$ + 7 | ||

b. | $y$ = $\sqrt{2x+5}$ | ||

c. | $y$ = $\sqrt{2x}$ + 1 | ||

d. | $y$ = $\sqrt{x+7}$ |

Consider the function

Consider the function

Consider the function

Consider the function

Correct answer : (4)

8.

Which of the following functions best represents the graph?

a. | $\frac{\sqrt{x}-2}{x}$ | ||

b. | $\sqrt{x-4}$ | ||

c. | $\frac{\sqrt{x-4}}{x}$ | ||

d. | $\sqrt{4x}$ - 1 |

Correct answer : (1)

9.

The period T in seconds and the length L in inches of the pendulum are related as T = 2$\pi $$\sqrt{\frac{\mathrm{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 |

T

[Square on both sides.]

384 · T

[Multiply both sides with 384.]

L =

[Divide both sides by (2

L =

[Substitute 6 for T.]

L = 350.17 inches.

The length of the pendulum = 350.17 inches.

Correct answer : (1)

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 $ $r$ $\sqrt{{r}^{2}+{h}^{2}}$.

Use the formula

a. | 5$\pi $ sq.cm. | ||

b. | 15$\pi $ sq.cm. | ||

c. | 8$\pi $ sq.cm. | ||

d. | 24$\pi $ sq.cm. |

= 3

[Replace

= 15

Correct answer : (2)