/sci/ - Science & Math

Hi /sci/, there's this thing that keeps bugging me about square rooting a decimal number between 1 and 0. When I keep square rooting, the number tends to 1.

I don't understand why this happens, I mean for fractions it's easy to explain since <span class="math"> \sqrt{\frac{1}{16}} = \frac{1}{4}[/spoiler] and the square root of that is <span class="math"> \frac{1}{2}[/spoiler]. The denominator keeps decreasing, but I can't figure out what happens to the irrational numbers inbetween 1 and 0.

Does anyone have a nice explanation?

Thank you for your time.

>in high school
>teacher teaches us that sqrt of a number, e.g 4 is +/- 2
>forget this on exam
>do not get A
>start college
>is taught math from a pro teacher
>learn that sqrt of a number is defined to only return the positive root, e.g sqrt(4) = 4
>learn that x^2 = 4 -> x=+/- 2, but that does not mean that sqrt(4) = +/- 4
>rage