Q:

Inequality question? If $x \lt y$, prove that $x^2 \lt y^2$

If $x \lt y$
Prove that 
$x^2 \lt y^2$
When x and y are real positive numbers

A:

Multiply $x<y$ by the positive numbers $x$ and $y$ in turn to get $xx<xy$ and $xy<yy$ so that
$$
xx<xy<yy
$$

