how do i find the square root of a non-perfect square (sorry if its the wrong sub for this)
In: Mathematics
It can be just guess work.
If you’re doing it in your head then pick the two perfect squares either side. Like for sqrt 110 I’d say I know it’s between 10 and 11 (100 and 121 respectively). So a first guess would be 10.5. try that and second guess will.either be a bit higher or lower
There are more sophisticated methods to guess better. Ultimately they’re stil just approximations.
One other way is fancy maths simplification. So sqrt(200) = sqrt(100*2)=sqrt(100)*sqrt(2)=10*sqrt(2). So if I know sqrt(2) I can also tell you sqrt(200). It’s still guesswork to get the first one, but from there it gets easier.
I have a feeling there is some fancy work you can do with log tables, but for the life of me I can work out how to type it when I’m on mobile.
Edit: I think I have the log answer.
So, say x^2 = 200.
Log of both sides: log(X^2) = log(200)
Simplify: 2log(X)=log(200).
Log(X)= log(200)/2
Solve for X: X= 10^(log(200)/2)
Some clever people have calculated all the log values, it’s in a log table. So you can just read the number off for log(200). Then you have a clear sum to calculate.
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