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How do you arrive at a square root?

ne way is to iterate: Make a guess, square it, compare it with the value you're taking the root of, and refine your guess based on this comparison. Repeat until you're as close as you need to be, or until your guess-refining procedure fails to improve the guess.

A more general way is to take advantage of a property of the logarithm function:

a ln(x) = ln(x^a)


x^a = e^(a ln(x))

The advantage of this approach is that you can use it to do all kinds of roots and raise numbers to non-integral powers. This is how slide rules took roots.

Of course, you have to be able to do logarithms.


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