How to find the number of digits of square root of a number ?
Here we are going to see how to find the number of digits of square root of a number.
Let us observe the following pattern.
Perfect squares

Square root

Number of digits

1 16 36 81 
1 4 6 9 
One digit 
100 225 2025 7396 9801 
10 15 45 86 99 
Two digits 
10,000 14,641 2,97,025 9,98,001 
100 121 545 999 
Three digits 
10,00,000 15,00,625 7,89,96,544 999,80,001 
1000 1225 8888 9999 
Four digits 
By observing the above tables, we come to know that
From the table, we can also infer that
(i) If a perfect square has ‘n’ digits where n is even, its square root has
n/2 digits.
(ii) If a perfect square has ‘n’ digits where n is odd, its square root has
(n + 1)/2 digits.
Let us look into some examples to understand the above concept.
Example 1 :
Find the number of digits in the square root of the following number (without any calculation)
36
Solution :
Number of digits in the given number = 2 (Even)
Formula to find the number of digits in the square root of the given number = n/2
= 2/2
= 1
Hence the square root of 36 will be the one digit number.
Example 2 :
Find the number of digits in the square root of the following number (without any calculation)
144
Solution :
Number of digits in the given number = 3 (Odd)
Formula to find the number of digits in the square root of the given number = (n + 1)/2
= (3 + 1)/2
= 4/2
= 2
Hence the square root of 144 will contain two digits.
Example 3 :
Find the number of digits in the square root of the following number (without any calculation)
4489
Solution :
Number of digits in the given number = 4 (Even)
Formula to find the number of digits in the square root of the given number = n/2
= 4/2
= 2
Hence the square root of 4489 will contain two digits.
Example 4 :
Find the number of digits in the square root of the following number (without any calculation)
27225
Solution :
Number of digits in the given number = 5 (Odd)
Formula to find the number of digits in the square root of the given number = (n + 1)/2
= (5 + 1)/2
= 6/2
= 3
Hence the square root of 27225 will contain three digits.
Example 5 :
Find the number of digits in the square root of the following number (without any calculation)
390625
Solution :
Number of digits in the given number = 6 (Even)
Formula to find the number of digits in the square root of the given number = n/2
= 6/2
= 3
Hence the square root of 390625 will contain three digits.
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