Giải thích các bước giải:
a.Ta có:
$\sqrt{9-\sqrt{17}}\cdot \sqrt{9+\sqrt{17}}=\sqrt{(9-\sqrt{17})(9+\sqrt{17})}$
$\to \sqrt{9-\sqrt{17}}\cdot \sqrt{9+\sqrt{17}}=\sqrt{9^2-(\sqrt{17})^2}$
$\to \sqrt{9-\sqrt{17}}\cdot \sqrt{9+\sqrt{17}}=\sqrt{81-17}$
$\to \sqrt{9-\sqrt{17}}\cdot \sqrt{9+\sqrt{17}}=\sqrt{64}$
$\to \sqrt{9-\sqrt{17}}\cdot \sqrt{9+\sqrt{17}}=8$
b.Ta có:
$\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}$
$=\sqrt{5-2\sqrt{5}\cdot\sqrt{3}+3}-\sqrt{5+2\sqrt{5}\cdot\sqrt{3}+3}$
$=\sqrt{(\sqrt{5}-\sqrt{3})^2}-\sqrt{(\sqrt{5}+\sqrt{3})^2}$
$=(\sqrt{5}-\sqrt{3})-(\sqrt{5}+\sqrt{3})$
$=-2\sqrt{3}$
