how do i find the square root of a non-perfect square (sorry if its the wrong sub for this)
In: Mathematics
There are many methods. They tend to be recursive. Let me give you a simple one.
I want the square root of ten. I’m gonna use the ‘halfway guess and check’ method.
I know it’s bigger than zero and less than ten. Halfway between is five. Let’s square five. Twenty-five. Too big.
I know it’s bigger than 0 and less than 5. Halfway between is 2.5. Let’s square that. 6.25. Too small.
We know it’s bigger than 2.5 but less than 5. Halfway between is 3.75. Square that. 14.0625. Too big.
So it must be bigger than 2.5 but less than 3.75.
I’m done narrating. I’ll shorthand the steps.
3.125^2 = 9.76
Too small.
3.125<x<3.75
3.4375^2 = 11.816
Too big.
3.125<x<3.4375
3.28125^2 = 10.7666
Too big.
3.125<x<3.28125
I could keep doing this forever. I’ll get pretty close eventually. More efficient methods exist, but this one is nice and simple. Computers can do it ten thousand times in an instant, and that’s how my phone found the square root of ten (to within several decimal places): 3.16227766017
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