#### notes

Find the square of 23 so quickly . The answer is not so easy and we may need to multiply 23 by 23. There is a way to find this without having to multiply 23 × 23.

We know 23 = 20 + 3

Therefore `23^2`

= `(20 + 3)^2` = 20(20 + 3) + 3(20 + 3)

= `20^2 + 20 × 3 + 3 × 20 + 3^2`

= 400 + 60 + 60 + 9 = 529

**1) Other patterns in squares :**

Consider a number with unit digit 5, i.e., a5

`(a5)^2 = (10a + 5)^2`

= 10a(10a + 5) + 5(10a + 5)

= `100a^2 + 50a + 50a + 25 `

= 100a(a + 1) + 25

= a(a + 1) hundred + 25

Consider the following pattern:

252 = 625 = (2 × 3) hundreds + 25

352 = 1225 = (3 × 4) hundreds + 25

#### Shaalaa.com | Finding the Square of a Number - Other Patterns in Squares

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