To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)

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.


Correct answer : (3)
 2.  
Find the value of n, if 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.


Correct answer : (3)
 3.  
If 7n = 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.


Correct answer : (3)
 4.  
Approximate 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.


Correct answer : (2)
 5.  
Approximate 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.


Correct answer : (2)
 6.  
Choose the point that represents 2 on the number line.


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


Answer: (c)


Correct answer : (3)
 7.  
Choose the point that represents 5 on the number line.

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


Answer: (a)


Correct answer : (1)
 8.  
Identify the square root that the point represents on the number line.


a.
8
b.
19
c.
26
d.
6


Answer: (b)


Correct answer : (2)
 9.  
Choose the point that represents 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.


Correct answer : (2)
 10.  
Find the estimate of 850.
a.
25
b.
32
c.
29
d.
20


Answer: (c)


Correct answer : (3)

*AP and SAT are registered trademarks of the College Board.