Question

[Hotboy nguyên]

Tính

a) \(\left(\dfrac{3}{2}\sqrt{6}+2\sqrt{\dfrac{2}{3}}+4\sqrt{\dfrac{3}{2}}\right)\times\left(2\sqrt{\dfrac{2}{3}}-\sqrt{12}-\sqrt{6}\right)\)

b) \(\sqrt{6-2\sqrt{5}}-\sqrt{6+2\sqrt{5}}\)

c) \(\left(\sqrt{11+2\sqrt{24}}-\sqrt{11-2\sqrt{24}}\right):2\sqrt{3}\)

d) \(\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}\)

e) \(\sqrt{5+6\sqrt{2}}-\sqrt{9-6\sqrt{2}}-\sqrt{21-12\sqrt{3}}\)

f) \(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)

Answer 1

[Nguyễn Lê Phước Thịnh]

b: \(=\sqrt{5}-1-\sqrt{5}-1=-2\)

c: \(=\dfrac{\left(2\sqrt{2}+\sqrt{3}-2\sqrt{2}+\sqrt{3}\right)}{2\sqrt{3}}=1\)

d: \(=\dfrac{\sqrt{6-2\sqrt{5}}-\sqrt{6+2\sqrt{5}}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{5}-1-\sqrt{5}-1}{\sqrt{2}}=-\sqrt{2}\)