how to find square root of a number ?

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 One method is to calculate the square root of a number is by performing prime factorisation of the number.

To find the square root 676 first of all the prime factorisation of this number is done. This can be done as:
 
Second method is by long division method
Example:
Find the square root of the number 4096 using division method.
Solution:
Process:
1. Put a dot on the digit in the units place.
2. Put dots on the numbers leaving digit form right to left.
3. First take down two numbers from left to right of the number. in this case it is 40.
4. Consider the perfect square number which is very near to 40. Here it is 36.
5. Then write down its square root namely 6 as divisor and also in the place of quotient.
6. Find the product of 6 and 6 which is 36. So write down 36 below the number 40 of the dividend.
7. Subtract 36 form 40, write down the remainder so write down 36 below the number 40 of the dividend.
8. Now bring down the digits up to the next dot, they are 96, write 96 beside 4 you get 496.
9. Double the previous quotient namely 6 you get 2*6 = 12.
10. Divide the two digits of the number from left to right. So obtained in step 8 by 12, you get 4.
11. Write 4 by the side of 12 to make the divisor 124.
12. Put 4 by the side of 6 the quotient to get 64.
13. Multiply 124 by 4, the product is 496.
14. Subtracting 496 from 496, you get zero as the remainder.

 Since the remainder is zero the process of extracting square root of 4096 is completed.
 Ö4096 = 64.

Verification:
64 * 64 = 4096.
 64 is the square root of 4096.



 
Thus, the square root of 676 is 26
 
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