functional analysis - $f_nto f$ in $L^1$ $implies$ $sqrt{f_n}tosqrt{f}$ in $L^2$?

Suppose that $\{f_n\}$ is a sequence of measurable functions converging to $f$ in $L^1(\mathbb{R}^n)$. Is it true that $\sqrt{f_n}$ converges to $\sqrt{f}$ in $L^2(\mathbb{R}^n)$?

If this is true then I would need to show that $$\int \sqrt{f_n}\sqrt{f}\to\int f.$$

Could someone help.

Answer

$$\left(\sqrt{f_n}-\sqrt{f}\right)^2\leqslant|f_n-f|$$