$a)\left(\sqrt{21}-\sqrt{20}\right)\left(\sqrt{21}+\sqrt{20}\right)={\sqrt{21}}^2-{\sqrt{20}}^2=21-20=1$

$b)\sqrt{\sqrt{13}+2}\cdot \sqrt{\sqrt{13}-2}=\sqrt{\left(\sqrt{13}+2\right)\left(\sqrt{13}-2\right)}=$

$=\sqrt{{\sqrt{13}}^2-2^2}=\sqrt{13-4}=\sqrt{9}=3$

$c)\sqrt{5\sqrt{2}+7}\cdot \sqrt{5\sqrt{2}-7}=\sqrt{\left(5\sqrt{2}+7\right)\left(5\sqrt{2}-7\right)}=$

$=\sqrt{{\left(5\sqrt{2}\right)}^2-7^2}=\sqrt{25\cdot 2-49}=\sqrt{50-49}=\sqrt{1}=1$