The value of $\sqrt{1+1}$ is . . . . . . (Rational,Irrational,Integer).

The number $0.01111...$ is a type of........

The value of $\sqrt{1+1}$ is.......

$\pi$ is a . . . . . . type of number. (Rational,Irrational,Whole number)

Prove that $\sqrt{p}+\sqrt{q}$ is irrational,where $p$ and $q$ are distinct prime numbers.

The following real number is expressed in decimal form. Determine whether it is rational or not. If it is rational,express it in the form of $\frac{p}{q}$. $0.02003000400005 \ldots$