Number = 3

Square of number = 3 2

        = 3 × 3

        = 9

Square numbers is a number which we get when a number is multiplied by itself 2 times.

Here, 9 is a square number

They are sometimes also called perfect squares

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Let’s do some examples

Number

Square

1

1 × 1 = 1

2

2 × 2 = 4

3

3 × 3 = 9

4

4 × 4 = 16

5

5 × 5 = 25

6

6 × 6 = 36

7

7 × 7 = 49

8

8 × 8 = 64

9

9 × 9 = 81

10

10 × 10 = 100

Thus, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 are square numbers

 

Finding Square of a Large Number

Find 23 2

  23 2 = 23 ×  23

 = (20 + 3) ×  (20 + 3)

 = 20 ×  (20 + 3) + 3 ×  (20 + 3)

         = 20 ×  20 + 20 ×  3 + 3 × 20 + 3 × 3

        = 400 + 60 + 60 + 9

        = 529

 

Find 39 2

  39 2 = 39 ×  39

 = (40 – 1) ×  (40 – 1)

 = 40 × (40 – 1) – 1 ×  (40 – 1)

 = 40 × 40 + 40 × (–1) – 1 × 40 – 1 × (–1)

 = 1600 – 40 – 40 + 1

 = 1601 – 40 – 40

 = 1601 – 80

 = 1521

 

Is 1 a square number?

Square numbers is a number which we get when a number is multiplied by itself 2 times.

So, 1, 4, 9, 16, 25, 36, 49,  … are square numbers

∴ 1 is a square number

  1. Chapter 6 Class 8 Squares and Square Roots
  2. Concept wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.