Answer
$\sqrt{21}-\sqrt{3}-\sqrt{35}+\sqrt{5}$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL Method and the properties of radicals, the expression $
\left( \sqrt{3}-\sqrt{5} \right)\left( \sqrt{7}-1 \right)
$ is equivalent to
\begin{array}{l}
\sqrt{3}(\sqrt{7})+\sqrt{3}(-1)-\sqrt{5}(\sqrt{7})-\sqrt{5}(-1)
\\\\=
\sqrt{21}-\sqrt{3}-\sqrt{35}+\sqrt{5}
.\end{array}
