Question

M = \(\frac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}:\frac{1}{\sqrt{6}}\)

N = \(\frac{6}{1+\sqrt{7}}+\frac{1}{\sqrt{7}}\)

O = \(\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2+\sqrt{2}}{1+\sqrt{2}}-\frac{1}{2-\sqrt{3}}\)

Answer 1

\(M=\frac{\sqrt{6}\left(\sqrt{3}-\sqrt{2}\right)}{\sqrt{3}-\sqrt{2}}:\frac{1}{\sqrt{6}}=\sqrt{6}.\sqrt{6}=6\)

\(N=\frac{6\left(\sqrt{7}-1\right)}{\left(\sqrt{7}+1\right)\left(\sqrt{7}-1\right)}+\frac{\sqrt{7}}{7}=\frac{6\left(\sqrt{7}-1\right)}{6}+\frac{\sqrt{7}}{7}=\sqrt{7}-1+\frac{\sqrt{7}}{7}=\frac{8\sqrt{7}}{7}-1\)

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

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