# How do you find a one-decimal place approximation for #root2 65#?

##### 1 Answer

As a one-decimal digit approximation,

#### Explanation:

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