If \(\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})} = m +n\sqrt{6}\), find the values of m and n respectively.

Explanation

Rationalize \(\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})}\) and equate to \(m +n\sqrt{6}\). Such that m = -2, and n = 1.

Use  \(\sqrt{3}-2\sqrt{2}\) as the conjugate for Rationalization

\(\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})}\) X  \(\frac{(\sqrt{3}-2\sqrt{2})}{(\sqrt{3}-2\sqrt{2})}\)

\(\frac{6 - 4\sqrt{6} - \sqrt{6} + 4}{3 - 2\sqrt{6} + 2\sqrt{6} - 8}\)

=\(\frac{10 - 5\sqrt{6}}{-5}\)

= -2 + \(\sqrt{6}\) = \(m +n\sqrt{6}\)

∴ m = -2 and n = 1

There is an explanation video available .