# Finding Square Root Of A Number By Division Method

Any number can be expressed as a product of prime numbers. This method of representation of a number in terms of the product of prime numbers is termed as prime factorization method. It is the easiest method known for the manual calculation of the square root of a number. But this method becomes tedious and tiresome when the number involved is large. In order to overcome this problem, we use the long division method. The numbers of digits in a perfect square are very significant for calculating its square root by long division method.

Consider the following method for finding the square root of a number. It is explained with the help of an example for a clear understanding.

## Square root of a number by long division method

1. Taking 484 as the number whose square root is to be found. Place a bar over the pair of numbers starting from the unit’s digit. In case of an odd number the leftmost digit will also have a bar, $\overline{4}$  $\overline{8 4}$ .
2. Take the largest number as the divisor whose square is less than or equal to the number on the extreme left. The number on the extreme left is the dividend. Divide and write the quotient. Here the quotient is 2 and the remainder is 0.
3. We then bring down the number which is under the next bar to the right side of the remainder, in this case, we bring down 84. Now, 84 is our new dividend.
4. Now double the value of the quotient and enter it with a blank on the right side.
5. Now we have to select the largest digit for the unit place of the divisor (4_) such that the new number, when multiplied by the new digit at unit’s place, is equal to or less than the dividend (84).

In this case,  42 × 2 = 84. So the new digit is 2.

1. The remainder is 0 and we have no number left for multiplication, Therefore,

$\sqrt{484}$ = 22
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