# How accurate is the square root of a number?

This may sound like a silly question but: How accurately has the squareroot of numbers like 2,3,5 etc. been measured?
When you type it into a calculator it gives you an answer with a certain amount of decimal points,
the calculator is of course software programmed by a group of people who can't possibly
know the square root of 2 to the last descimal point, so is it
correctly assumed that you will never be able to define the square root of a number like 2,3,5 to the last
decimal point because the number of descimal points of 2,3,5 goes to infinity?
So the square root of 2 is undefined to the last descimal point.

phinds
Gold Member
2019 Award
You are correct. The square root of some numbers is an infinite string of digits and thus literally cannot be known to "full" precision. It isn't something that is, as you stated, "measured", it is calculated and it can be calculated to as many digits as you wish but that's a waste of time.

pbuk