How to explain to a 14-year-old that $\sqrt{(-3)^2}$ isn't $-3$? I had this problem yesterday. I tried to explain to the kid this: $$\sqrt{(-3)^2} = 3,$$ and he immediately said: "My teacher told us that we can cancel the square with the square root, so it's $$\sqrt{(-3)^2} = -3."$$
He has a lot of problems with maths, and I don't know how I can explain to him this as easily as possible. He still thinks that I lied him.
Thank you.

It's not quite right to say that the square and the square root cancel each other (in fact, this example demonstrates that nicely!)
For this problem, we have $\sqrt{(-3)^2} = \sqrt{9} = 3$.  But why are these the right two steps?  Because we evaluate functions from the inside out.  Thus, the first step is to square the $-3$.  The second step is a matter of convention: the square root of a positive number is taken to be the positive root (one could choose the negative root, but that would be a different function...)
