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
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