HOW TO FIND THE NUMBER OF DIGITS OF SQUARE ROOT OF A NUMBER

Observe the following pattern.

By observing the above tables, we come to know that 

• Single or double digit numeral has single digit in its square root.
• 3 or 4 digit numeral has 2 digits in its square root.
• 5 or 6 digit numeral has 3 digits in its square root.
• 7 or 8 digits numeral has 4 digits in its square root.

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

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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