Square Roots of Perfect Squares

Finding square root through repeated subtraction

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

The square root can be found through repeated subtraction. To find the square root of a number n:
Step 1: subtract successive odd numbers starting from one.
Step 2: stop when you get zero.

The number of successive odd numbers that are subtracted gives the square root of that number. Suppose we want to find the square root of 36.

  • 36-1=35
  • 35-3=32
  • 32-5=27
  • 27-7=20
  • 20-9=11
  • 11-11=0

Here 6 odd numbers (1, 3, 5, 7, 9, 11) are subtracted to from 36 to get 0.
So, the square root of 36 is 6.

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