How can one prove that $S( \mathbb{R}^{d}) $, the Schwartz space, is dense in $L^{2}(\mathbb{R}^{d}) $?

A slightly stronger result is that $C_{0}^{\infty}( \mathbb{R}^{d}) $, the set of infinitely differentiable functions with compact support, is dense in $L^{2}(\mathbb{R}^{d}) $, but I think this is probably easy to show once it has been proved that $S( \mathbb{R}^{d}) $ is dense in $L^{2}(\mathbb{R}^{d}) $.