0Every natural number squared can be written as the sum of consecutive odd natural numbers starting from zero. So for finding square root, we start subtraction from 1 and continue until it reaches zero. The number of steps to reach zero is the square root.
Example 1) Find the square root of 144 by the subtraction method.
We solve it like this:- 144-1=143,143-3=140,140-5=135,135-7=128,128-9=119,119-11=108,108-13=95,
95-15=80,, 80-17=63, 63-19=44, 44-21=23,23-23=0
Here we see there are 12 steps to reach zero. So 144=12^2 and square root of 144=12.
Example 2) Find the square root of 100 by the subtraction method.
We start from 100-1=99,99-3=96,96-5=91,91-7=84,84-9=75,75-11=64,64-13=51,51-15=36,36-17=19.
19-19=0
Here we see there are 10 steps to reach zero.
So the square root of 100=10
