Finding Square root through Repeated Subtraction

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Square root through Repeated Subtraction We know that Every perfect square is the sum of consecutive odd numbers starting from 1. To find Square root, we successively subtracting odd numbers starting from 1. If you reach exactly 0, the number is a perfect square. The number of subtractions you performed is its square root. Let’s some examples Find Square root of 25 We repeatedly subtract consecutive odd numbers starting from 1 25 − 1 = 24 24 − 3 = 21 21 − 5 = 16 16 − 7 = 9 9 − 9 = 0 Since, after subtracting 5 times, we obtained 0. ∴ √𝟐𝟓 = 5 Find √𝟖𝟏 We repeatedly subtract consecutive odd numbers starting from 1 81 − 1 = 80 80 − 3 = 77 77 − 5 = 72 72 − 7 = 65 65 − 9 = 56 56 − 11 = 45 45 − 13 = 32 32 − 15 = 17 17 − 17 = 0 Since, after subtracting 9 times, we obtained 0. ∴ √𝟖𝟏 = 9 But, if we take a big number, like 729. How would we find square root? We do it by Prime Factorization