Square root operation and scales

1. Jul 20, 2009

IsrTor

this is a strange problem easy to solve but I am having trouble understanding it intuitivly.

Assume we choose a location point and name it 0. Next, in arbitrary direction and distance we place the number 1. Hence, we have created a scale(number line) that extends as much as we like. Now we consider the square root operation(no need to state it). Suppose I choose a number thats hasn't a whole root... for instance lets choose 8.

Now consider this carefully: We take our scale and we stretch(by a factor of 8) so that the orgin remains unchanged but now what used to be 1 is 8 and what used to be 8 is now 64. Now if we take the square root of 64 we get 8. But heres the problem, we mark the place where 8 was the square root and we squeeze the scale back down to its original size only now the place we marked as 8 which was the square root is not at 1 but rather about 2.828

( I figured out that square root of 64 is 8 and square root of 8 when rounded gives 2.828)
But this problem is showing something about the square root operation on different scales(on a scale transformation). If someone could help to understand the intuition here I would greatly appreciate.

2. Jul 21, 2009

queenofbabes

Your stretching transformation is linear, but the sqrt function isn't (just look at the graph y = sqrt x)

I think I understand what you're asking, but I'm rubbish with words >.<