Question

Write the lowest rationalising factor of :

3√2+2√332√+23√ is

Answer 1

The lowest rationalizing factor be of the type $a\sqrt{3}+b\sqrt{2};(3\sqrt{2}+2\sqrt{3})(a\sqrt{3}+b\sqrt{2})=3\ast 2\ast b+2\ast 3\ast a+2b\sqrt{6}+3a\sqrt{6}$.
To be rational, $2b\sqrt{6}=-3a\sqrt{6};\Rightarrow 3a=-2b$;
For the least value of rationalizing factor, $a=2,b=-3;i.e,2\sqrt{3}-3\sqrt{2}$