real analysis - If $f$ is absolutely continuous $sqrt(f)$ may not be

The problem reads:

Prove that if $ f:[0,1]\rightarrow(0,\infty) $ is absolutely continuous $ \sqrt{f} $ may not be.

I am having trouble figuring out how to show this. I found that $x^2\sin\left(\frac{1}{x^2}\right)$ is not absolutely continuous, but then I need to show that $\left[x^2\sin\left(\frac{1}{x^2}\right)\right]^2$ is absolutely continuous and I don't think that it is. Is there a more general way to show this or is there a counterexample that works?