The solution of the square root by long division of a) 308.0025 and b) 41616 is attached with the images.
Steps to find square root through long division :
1. Divide the digits of the number into pairs of segments starting with the digit in the units place. Let’s identify each pair and the remaining final digit(in case there is an odd count of digits in the number) as a segment.
2. After dividing the digits into segments, start from the leftmost segment. The largest number whose square is equal to or just less than the first segment is taken as the divisor and also as the quotient (so that the product is the square).
3. Subtract the square of the divisor from the first segment and bring down the next segment to the right of the remainder to get the new dividend.
For example:
4. Now, the new divisor is obtained by taking two times the previous quotient and concatenating it with a suitable digit which is also taken as the next digit of the quotient, chosen in such a way that the product of the new divisor and this digit is equal to, or just less than the new dividend.
5. Repeat steps (2), (3) and (4) till all the segments have been taken up. Now, the quotient so obtained is the required square root of the given number.
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