Question

Giúp tớ với:

A=\(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

B=\(\left(\sqrt{\sqrt{6}+\sqrt{3+2\sqrt{2}}}.\sqrt{3+\sqrt{2}}.\sqrt{\sqrt{6}-\sqrt{3+2\sqrt{2}}}\right)\)

C=\(\left(\sqrt{6}-\sqrt{2}\right)\left(10+5\sqrt{3}\right)\sqrt{2-\sqrt{3}}\)

Answer 1

\(B=\sqrt{\sqrt{6}+\sqrt{3+2\sqrt{2}}}\cdot\sqrt{3+\sqrt{2}}\cdot\sqrt{\sqrt{6}-\sqrt{3+2\sqrt{2}}}=\sqrt{6-\left(3+2\sqrt{2}\right)}\cdot\sqrt{3+\sqrt{2}}=\sqrt{3-2\sqrt{2}}\cdot\sqrt{3+\sqrt{2}}=\left(\sqrt{2}-1\right)\sqrt{3+\sqrt{2}}\)

\(C=\left(\sqrt{6}-\sqrt{2}\right)\left(10+5\sqrt{3}\right)\sqrt{2-\sqrt{3}}=\sqrt{2}\left(\sqrt{3}-1\right)\cdot5\left(2+\sqrt{3}\right)\sqrt{2-\sqrt{3}}=\sqrt{2}\left(\sqrt{3}-1\right)\cdot5\sqrt{2+\sqrt{3}}\cdot\sqrt{4-3}=5\left(\sqrt{3}-1\right)\cdot\sqrt{4+2\sqrt{3}}=5\left(3-1\right)=10\)