how to find square root of a number

Methods for finding square roots

1. By Prime factorization Method

1. Prime Factorized the number.
2. Make Pair of same factors.
3. If any number is not paired then the square root will not be a whole number.
4. Now for every pair of prime write a single digit. The resultant number will be the square root of the given number.

for example: taking the number 625
Prime factorization of this number will yield 625 = 5 x 5 x5 x5
There are two pairs of five here. Write a single 5 for each pair we will get 5 x 5 = 25 and hence 25 is the square root of 625.


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2. By some division method ( dont know the name of it)





1. Put the given number in the dividend position.

2. Starting from the rightmost digits in the number, make pairs. If the leftmost digit is single leave it as it is.

3. Now pick a number, the square of whom is just less than the left pair or leftmost number.
  Here 2 is ideal as the square of 2 is less than 6  but the square of next number 3,  happens to be 9 and is greater than 6.  
   Now put the square of 2 below the number 6 and subtract to get 2 as remainder.
  
        

4. Now, get the next pair and write it after the remainder.

                                                

5. Double the number used in first step. 
                           
                                                       

                         
6. Now find a number beginning with 4 and ending with a digit that if multiplied by the digit itself gives a number that either equal to the number obtained in step 4 or just less than that.

Example if we put 4 that the number formed is 44 and when forty four multiplied with 4 gives out 176 and now trying 5 then number is 45 and it is to be multiplied with 5 to get 225 and that;s the exact number we are looking for!