Check sibling questions

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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.