Question

is the square root of 22 rational or irrational

Answer 1

22 is not a perfect square...
\[\sqrt{a} \in \mathbb{Q} \text{ if } a \text{ is an integer square }\]
for example
\[\sqrt{9} =3 \text{ is rational } \\ \text{ but } \sqrt{2} \text{ is not rational }\]