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Square Roots - Finding Square Root by Division Method

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When the numbers are large, even the method of finding square root by prime factorisation becomes lengthy and difficult. To overcome this problem we use Long Division Method.
For this we need to determine the number of digits in the square root. See the following table:

Number  Square  

 

10

100 which is the smallest 3-digit perfect square 
31 961 which is the greatest 3-digit perfect square
32 1024 which is the smallest 4-digit perfect square
99 9801 which is the greatest 4-digit perfect square

The number of digits in the square root if a perfect square is a 3-digit or a 4-digit number. 
If a perfect square is a 3-digit or a 4-digit number, then its square root will have 2-digits. 
The smallest 3-digit perfect square number is 100 which is the square of 10 and the greatest 3-digit perfect square number is 961 which is the square of 31. The smallest 4-digit square number is 1024 which is the square of 32 and the greatest 4-digit number is 9801 which is the square of 99.

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