If √$x$ + √$y=7$ and √$x$ − √$y=1$, then $xy$ equals:

Treat √$x$ and √$y$ as the unknowns: adding gives 2√$x=8$, so √$x=4$ and √$y=3$. Then $x=16,y=9$ and $xy=144$. (12 is √$x$ · √$y$ = √$(xy)$, one square root short; 49 is $(\surd x+\surd y{)}^2.$)