How do you find a one-decimal place approximation for #root2 65#?
As a one-decimal digit approximation,
I am assuming of course that you can't use a calculator, otherwise the answer is: read it :)
So, you need an approximation, and a very simple way to find it is to try various numbers (of course with some wisdom, not just trying random numbers 'till you're lucky!): when you find a number which is smaller than the one you need, and one which is bigger, then surely the number you're looking for is between them.
Let's start searching the right integer: since
We can easy compute
I hope that at this point the routine is clear for any number of digits you like.
Just for completion, the "actual" square root is