# How to find square root of 274?

##### 1 Answer

Algebraically

You can calculate an approximation

#### Explanation:

If the radicand of a square root has square factors, then it can be simplified.

For example:

In the case of

So we can get

but that's not really simpler.

If we want to *approximate* the value of

Note that

Then we can iterate using a Newton Raphson method:

where

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: