Finding number of digits in square root (without calculation)

Let n = Number of digits of number

Let’s do some examples

Find number of digits in square root of 529.

Number of digits of 529 = n = 3

Since n is odd

∴ Number of digits in square root = (n  +   1)/2

      = (3 +  1)/2=4/2= 2

Find number of digits in square root of 100489.

Number of digits of 100489 = n = 6

Since n is even

∴ Number of digits in square root = n/2 

       = 6/2 = 3