Using the Cauchy–Schwarz inequality

Recall that the Cauchy–Schwarz inequality stats that for any two random variable \(X\) and \(Y\) one has that
\[ \mathbf E |XY| \leq \sqrt{\mathbf E [X^2]}\,\sqrt{  \mathbf E [Y^2]}\]

1. Use it to show that
   \[ \mathbf E |X| \leq \sqrt{\mathbf E [X^2]}\]