Is the square root a contraction? If yes, there should be only one fixed point; yet, there are two of them, 0 and 1! Thanks for help!
You’ve actually answered your own question: it’s not a contraction. I suspect, however, that what you’d really like is an example showing that it’s not a contraction. If $f(x)=\sqrt x$, how does $$\left|f\left(\frac14\right)-f(0)\right|$$ compare with $$\left|\frac14-0\right|\,?$$