How to find square root of 274?
You can calculate an approximation
If the radicand of a square root has square factors, then it can be simplified.
In the case of
So we can get
but that's not really simpler.
If we want to approximate the value of
Then we can iterate using a Newton Raphson method:
Actually, I prefer to keep the numerator and denominator of the rational approximation as separate integers and iterate as follows:
Stop when you think you have enough significant digits, then divide to get your approximation: