$\sqrt{2}$ is a . . . . . . number. (Rational,Irrational,Prime)

The following real number is expressed in decimal form. Determine whether it is rational or not. If rational,express it in the form of $\frac{p}{q}$. $5 . \overline{123456}$

The irrational number which is not a surd is ...............

Prove that $\sqrt{2}+\sqrt{3}$ is irrational.

Prove that: $\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2-\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2+\sqrt{3}}}=\sqrt{2}$

The rationalising factor of $5 \sqrt{2}$ is ..............