To find Square root,

we subtract consecutive odd numbers from number till we obtain 0.

 

Square root = Total numbers subtracted.

 

Let’s take an example

 

Suppose we need to find

√81

 

Square root of √81

  1. 81 − 1 = 80
  2. 80 − 3 = 77
  3. 77 − 5 = 72
  4. 72 − 7 = 65
  5. 65 − 9 = 56
  6. 56 − 11 = 45
  7. 45 − 13 = 32
  8. 32 − 15 = 17
  9. 17 − 17 = 0

Since, after subtracting 9 numbers, we obtained 0.

  ∴ 81   = 9

 

Square root of √81

  1. 81 − 1 = 80
  2. 80 − 3 = 77
  3. 77 − 5 = 72
  4. 72 − 7 = 65
  5. 65 − 9 = 56
  6. 56 − 11 = 45
  7. 45 − 13 = 32
  8. 32 − 15 = 17
  9. 17 − 17 = 0

 

But, if we take a big number, like 729.

How would we find square root?

We do it by prime factorization (link)

  1. Chapter 6 Class 8 Squares and Square Roots
  2. Concept wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.