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June 19

Square roots

I've always found these on the calculator but recently i wanted to learn the mechanics behind it. But everything ive found on it is just find the 2 natural squareroots on either side and then just guess until you are correct. Can it be true theres no real way to calculate it precisely but its just an elaborate guessing game?91.101.26.175 (talk) 20:47, 19 June 2019 (UTC)

There are efficient methods of square root computation. See Square root § Computation and Methods of computing square roots for more information. –Deacon Vorbis (carbon • videos) 20:59, 19 June 2019 (UTC)

If n is not a perfect square then you cannot calculate the value of √n exactly. But there are methods of approximating the square root to any required degree of accuracy which are much more efficient that the bisection method (which is my interpretation of what the OP means by "just guessing"). Gandalf61 (talk) 08:58, 27 June 2019 (UTC)

What is your first sentence supposed to mean? --JBL (talk) 02:08, 28 June 2019 (UTC)

It should become clear if you change the setting of your brain's math filter from extremely rigorous to moderately rigorous :) Count Iblis (talk) 14:51, 28 June 2019 (UTC)

What is the moderately rigorous sense in which 0.142857142857... is exact but [1; 2, 2, 2, ...] is not? --JBL (talk) 15:40, 28 June 2019 (UTC)