Answer
$21+4\sqrt{x}-x$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$, or the FOIL method, and the properties of radicals, the given expression, $
(3+\sqrt{x})(7-\sqrt{x})
,$ simplifies to
\begin{array}{l}\require{cancel}
3(7)+3(-\sqrt{x})+\sqrt{x}(7)+\sqrt{x}(-\sqrt{x})
\\\\=
21-3\sqrt{x}+7\sqrt{x}-x
\\\\=
21+4\sqrt{x}-x
.\end{array}
Note that all variables represent positive real numbers.
