Without using calculators & libraries find the square roots of the following numbers: 81 , 4 , 5 , 8 , 7
the first algorithm & the easiest used for approximating https://wikimedia.org/api/rest_v1/media/math/render/svg/bff86975b0e7944720b3e635c53c22c032a7a6f1 is known as the Babylonian method. there are other methods such Newton–Raphson methods etc
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https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method