Question

Tính :

a) \(\sqrt{3\sqrt{2}+2\sqrt{3}}.\sqrt{3\sqrt{2}-2\sqrt{3}}\)

b) \(\left(1-\sqrt{2}+\sqrt{3}\right)\left(1+\sqrt{2}-\sqrt{3}\right)\)

c) \(\left(5+4\sqrt{2}\right)\left(3+2\sqrt{1+\sqrt{2}}\right)\left(3-2\sqrt{1+\sqrt{2}}\right)\)

Answer 1

a)

\(M=\sqrt{3\sqrt{2}+2\sqrt{3}}\times\sqrt{3\sqrt{2}-2\sqrt{3}}\)

\(M^2=\sqrt{2\times3}\left(\sqrt{3}+\sqrt{2}\right)\times\sqrt{2\times3}\left(\sqrt{3}-\sqrt{2}\right)\)

\(=6\)

\(\Rightarrow M=\sqrt{6}\)

b)

\(\left(1-\sqrt{2}+\sqrt{3}\right)\left(1+\sqrt{2}-\sqrt{3}\right)\)

\(=1-\left(\sqrt{3}-\sqrt{2}\right)^2\)

\(=1-3+2\sqrt{6}-2=-4+2\sqrt{6}\)

c)

\(\left(5+4\sqrt{2}\right)\left(3+2\sqrt{1+\sqrt{2}}\right)\left(3-2\sqrt{1+\sqrt{2}}\right)\)

\(=\left(5+4\sqrt{2}\right)\left(9-4-4\sqrt{2}\right)\)

\(=25-32=-7\)