$\sqrt{289} + 1$ is ............

$\frac{p}{q}$ is a rational number and for non-negative integers $m$ and $n$,$q = 2^{m} 5^{n}$ if and only if the decimal form of $\frac{p}{q}$ is $\ldots \ldots \ldots \ldots$

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

If $\text{g.c.d.} (a, b) = b$,then $\text{l.c.m.} (a, b) = \dots$ (where,$a, b \in N$)

Prove that $21^{n}$ cannot end in zero for any natural number $n \in N$.

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