Square Roots Taken Repeatedly Date: 11/21/2002 at 22:43:29 From:
John Subject: Square Roots Why, when you repeatedly take the
square root of a whole number, do you end up with 1? For
example, if you take the square root of 10, and repeat taking
the square root, you will end up with 1. Thanks. Date:
11/21/2002 at 23:00:00 From: Doctor Ian Subject: Re: Square
Roots Hi John, Actually, you won't get all the way to one. The
only way you can get _exactly_ one by taking a square root is if
you start with 1. That is, sqrt(1) = 1 but sqrt(1 + something) =
(1 + something smaller) > 1 However, if you keep taking square
roots, a calculator will eventually be unable to represent
'something smaller', so it will _look_ as if it's telling you
that the value is 1. But it's not. It's just running out of
space to store all the zeros. That is, suppose you're taking
square roots, and you get to the point where the next square
root is 1.000000000000000000000000000000000000000000000000000000
0000000001 Most calculators would just th