a, Ta có : \(A=\sqrt{2}\left(\sqrt{8}-\sqrt{32}+3\sqrt{18}\right)\)
\(=\sqrt{16}-\sqrt{64}+3\sqrt{36}=4-8+3.6=14\)
b, Ta có : \(B=\sqrt{2}\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\)
\(=\sqrt{4}-\sqrt{2\left(3-\sqrt{5}\right)}=2-\sqrt{6-2\sqrt{5}}\)
\(=2-\sqrt{5-2\sqrt{5}+1}=2-\left(\sqrt{5}-1\right)=2-\sqrt{5}+1=3-\sqrt{5}\)
c, Ta có : \(C=\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)
\(=\frac{\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}}{\sqrt{2}}=\frac{\sqrt{7-2\sqrt{7}+1}-\sqrt{7+2\sqrt{7}+1}}{\sqrt{2}}=\frac{\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)^2}}{\sqrt{2}}\)
\(=\frac{\sqrt{7}-1-\sqrt{7}-1}{\sqrt{2}}=\frac{-2}{\sqrt{2}}=-\sqrt{2}\)
d, Ta có : \(D=\sqrt{\sqrt{3}-\sqrt{2}}-\sqrt{\sqrt{3}+\sqrt{2}}\)
\(=-\sqrt{\left(\sqrt{\sqrt{3}-\sqrt{2}}-\sqrt{\sqrt{3}+\sqrt{2}}\right)^2}\)
\(=-\sqrt{\sqrt{3}-\sqrt{2}-2\sqrt{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}+\sqrt{3}+\sqrt{2}}\)
\(=-\sqrt{2\sqrt{3}-2}=-\sqrt{2\left(\sqrt{3}-1\right)}\)
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