Why are surds put on the numerator in the final answer when it is a fraction.

Question

I have learnt that a fraction with a surd in its most simplest form should have the surd in the numerator and not the denominator? Why is it convention not to leave the surd on the denominator? Is it just arbitrary convention or does it have an actual purpose?

Answer 1

It is a good practice motivated, at elemental level, by the fact that, for fractions with irrational only at the numerator, we can easily apply the distributive property if it is the case, as: $$ \frac{3}{\sqrt{2}}+2\sqrt{2}=\frac{3}{2}\sqrt{2}+2\sqrt{2}=\frac{7}{2}\sqrt{2} $$