Explain to me like I’m 5, how to determine the square root of a random positive number. And I don’t mean common sense like 16=4, I need to understand the logic.
In: 6
There are many ways to find an approximation of a square root. One of the oldest known and easiest to understand is the Babylonian method. If you are trying to find the square root of N, start with some guess x. Then take the average of x and N/x and that then becomes your new value for x. Repeat those steps until the difference between x and N/x is small enough that you’re satisfied with the level of precision. This works because if x is too small, N/x will be too large, and if x is too large then N/x will be too small. The true value is always somewhere in between. It will actually work with any starting value of x, but it will converge on the true value faster if you start with a good approximation.
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