rút gọn
a)\(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)
b)\(\sqrt{3}-\sqrt{2}-\sqrt{\sqrt{3}-\sqrt{2}}\)
c)\(\sqrt{4+2\sqrt{2}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)
d)\(\left(\sqrt{14}-\sqrt{10}\right)\left(\sqrt{6+\sqrt{35}}\right)\)
e)\(\sqrt{11-4\sqrt{7_{ }}}-\sqrt{2}.\sqrt{8+3\sqrt{7}}\)
a: \(=\dfrac{\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}}{\sqrt{2}}\)
\(=\dfrac{\sqrt{7}-1-\sqrt{7}-1}{\sqrt{2}}\)
\(=-\dfrac{2}{\sqrt{2}}=-\sqrt{2}\)
c: \(=\sqrt{4+2\sqrt{2}}\cdot\sqrt{4-\left(2+\sqrt{2}\right)}\)
\(=\sqrt{4+2\sqrt{2}}\cdot\sqrt{2-\sqrt{2}}\)
\(=\sqrt{2\left(\sqrt{2}+1\right)\cdot\sqrt{2}\cdot\left(\sqrt{2}-1\right)}=\sqrt{2\sqrt{2}}\)
d: \(=\left(\sqrt{7}-\sqrt{5}\right)\left(\sqrt{12+2\sqrt{35}}\right)\)
\(=\left(\sqrt{7}-\sqrt{5}\right)\left(\sqrt{7}+\sqrt{5}\right)\)
=7-5=2
