# Square Roots Practice Problems

Square Roots Practice Problems
• Page 1
1.
Find the cube root of 125.
 a. 25 b. 50 c. 5 d. 10

#### Solution:

Cube root of 125 = 1253

1253 = (125)13
[an = (a)1n]

= (53)13
[125 can be written as 5 × 5 × 5 = 53]

= (5)3 ×13
[(an)m = amn]

= 5

So, cube root of 125 is 5.

2.
Find the value of $n$, if $\sqrt{n}$ = 13.
 a. 121 b. 151 c. 169 d. 159

#### Solution:

n = 13

(n)2 = (13)2
[Square both sides.]

n = 169

So, the value of n is 169.

3.
If 7$n$ = 49, then find the value of $n$.
 a. 3 b. 7 c. 2 d. 5

#### Solution:

7n = 49

7n = 72

n = 2
[Powers are equal, when bases are equal.]

So, the value of n is 2.

4.
Approximate $\sqrt{21}$ to the nearest tenth.
 a. 3 b. 4.6 c. 4.5 d. 3.5

#### Solution:

Find the square root of 21 using a calculator.

From the calculator, the value of 21 = 4.582575694.

In the decimal number, the digit in the tenths place is 5 and the digit in the hundredths place is 8.

Since 8 is greater than 5, the decimal 4.582 is closer to 4.6 than to 4.5.

Therefore, 21 approximated to nearest tenth is 4.6.

5.
Approximate $\sqrt{218}$ to the nearest tenth.
 a. 14.42 b. 14.8 c. 14.7 d. 14

#### Solution:

Find the square root of 218 using a calculator.

From the calculator, the value of 218 = 14.76482306023.

In the decimal number, the digit in the tenths place is 7 and the digit in the hundredths place is 6.

Since 6 is greater than 5, the decimal 14.764 is closer to 14.8 than to 14.7.

Therefore, 218 approximated to nearest tenth is 14.8.

6.
Choose the point that represents $\sqrt{2}$ on the number line.

 a. O b. M c. N d. P

7.
Choose the point that represents $\sqrt{5}$ on the number line.

 a. O b. S c. P d. R

8.
Identify the square root that the point represents on the number line.

 a. $\sqrt{8}$ b. $\sqrt{19}$ c. $\sqrt{26}$ d. $\sqrt{6}$

9.
Choose the point that represents $\sqrt{6}$ on the number line.

 a. S b. Q c. P d. R

#### Solution:

6 lies between the perfect squares 4 and 9.

6 lies between 4 and 9.

4 = 2 and 9 = 3.

6 lies between 2 and 3 on the number line.

So, the point Q represents 6 on the number line.

Find the estimate of $\sqrt{850}$.