#### notes

The sum of the first n odd natural numbers is `n^2`.

Every square number can be expressed as a sum of successive odd natural numbers starting from 1.

Consider `sqrt 81`. Then,

(i) 81 – 1 = 80 (ii) 80 – 3 = 77 (iii) 77 – 5 = 72 (iv) 72 – 7 = 65 (v) 65 – 9 = 56 (vi) 56 – 11 = 45 (vii) 45 – 13 = 32 (viii) 32 – 15 = 17 (ix) 17 – 17 = 0

From 81 we have subtracted successive odd numbers starting from 1 and obtained 0 at `9^(th)` step.