"Why do I always get 1 when I keep hitting the square root button on my calculator?" I asked myself this question when I was a young boy playing around with the calculator.

Today, I think I know the answer, but I'm not sure whether I'd be able to explain it to a child or layman playing around with a calculator.

Hence I'm interested in answers suitable for a person that, say, knows what the square root of a square number is, but doesn't know about sequences, functions, convergence and the like.
Here is how I had justified it to myself when I was a kid (I was convinced :-))

If $x > 1$ then $\sqrt x > 1$ and $x > \sqrt x$.

So we keep reducing the number while still being $> 1$.

Also, we cannot end up at a number $>1$ as then taking the square root would reduce it.

If we do end up at $1$, we stay there. Since the calculator has a limited precision, we end up at $1$, and pretty quickly.

Of course, the assumption here is that we do end up somewhere :-) 
(Which seemed justified by the fact that the first non-zero digit after the decimal point always seemed to reduce)
if(x == 0): sqrt(x) == 0
if(0 &lt; x &lt; 1): x &lt; sqrt(x) &lt; 1
if(x == 1): sqrt(x) == 1
if(1 &lt; x ): 1 &lt; sqrt(x) &lt; x


Except for the cases x == 0 and x == 1, x != sqrt(x) so it must move, and it must move towards 1, so it will approach 1 to any accuracy you choose.