Solved Examples and Worksheet for Identifying Square and Cube Roots of a Numbers

Q1Evaluate: 25
A. ±4
B. 5
C. 6
D. 25

Step: 1
25 = 52 = 5
Q2Find the square root of 25.

A. 5
B. 6
C. 7
D. 4

Step: 1
25
[Represent the square root using the radical symbol.]
Step: 2
= (5)2
[As 25 can be written as 52.]
Step: 3
= 5
Step: 4
So, the square root of 25 is 5.
Q3What is the simplest form of - 169 ?
A. - 169
B. - 13
C. 14
D. - 14

Step: 1
- 169
[Original expression.]
Step: 2
= - (13 × 13)
[Factor 169 as 13 × 13.]
Step: 3
= - 132

Step: 4
= - 13

Correct Answer is :   - 13
Q4Simplify: - 144
A. -12
B. - 14
C. - 11
D. None of the above

Step: 1
- 144
[Original numerical expression.]
Step: 2
= - 12 × 12
[Write 144 as perfect square factors.]
Step: 3
= - 12
[Find the square root.]
Q5Find the square root of 225.
A. 18
B. 22
C. 15
D. 13

Step: 1
225 can be written as 15 × 15.
Step: 2
225 = 152
Step: 3
Square root of 225 = 15.
Step: 4
225 =15
Q6Find the square root of 9025.

A. 25
B. 35
C. 18
D. 95

Step: 1
9025 can be written as 95 × 95.
Step: 2
9025 = 952
Step: 3
Square root of 9025 = 95.
Step: 4
9025 =95
Q7 Estimate the cube root of 29.
A. 3.5
B. 4.5
C. 3
D. 4

Step: 1
Cube of 3 = 3 × 3 × 3 = 27.
Step: 2
Cube root of 27 = 3.
Step: 3
Cube of 4 = 4 × 4 × 4 = 64.
Step: 4
Cube root of 64 = 4.
Step: 5
29 is closest to 27 than 64.
Step: 6
So, cube root of 29 is about 3.
Q8 Estimate the cube root of 65.

A. 5
B. 4.5
C. 6
D. 4

Step: 1
Cube of 4 = 4 × 4 × 4 = 64.
Step: 2
Cube root of 64 = 4.
Step: 3
Cube of 5 = 5 × 5 × 5 = 125.
Step: 4
Cube root of 125 = 5.
Step: 5
65 is closest to 64 than 125.
Step: 6
So, cube root of 65 is about 4.
Q9Find the cube root of 1331.
A. 12.1
B. 12
C. 9
D. 11

Step: 1
Cube root of 1331 = 13313
Step: 2
13313 = (1331)13
[an = (a)1n]
Step: 3
= (113)13
[1331 can be written as 11 × 11 × 11 = 113]
Step: 4
= (11)3 ×13
[(an)m = amn]
Step: 5
= 11
Step: 6
So, cube root of 1331 is 11.
Q10Find the square root of 625.

A. 23
B. 24
C. 15
D. 25

Step: 1
The square root of 625 = 625
Step: 2
= 25 × 25

Step: 3
= 252

Step: 4
= 25

Step: 5
Therefore, the square root of 625 is 25.
Q11Find the square root of 729.

A. 27
B. 28
C. 25
D. 26

Step: 1
The square root of 729 = 729
Step: 2
= 27 × 27

Step: 3
= 272

Step: 4
= 27

Step: 5
Therefore, the square root of 729 is 27.
Q12Find the square root of 2209.
A. 57
B. 47
C. 49
D. 39

Step: 1
The square root of 2209 = 2209
Step: 2
= 47 × 47

Step: 3
= 472

Step: 4
= 47

Step: 5
Therefore, the square root of 2209 is 47.