Question

State whether the following number is rational.
If rational, then enter $1$ and if false then enter $0$.

${\left(\frac{3}{2\sqrt{2}}\right)}^2$.

Answer 1

$(\frac{3}{2\sqrt{2}}{)}^2=\frac{9}{8}$

As $\frac{9}{8}$ is an irrational number, (which is in the form of $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$,

therefore given number is a rational number.

Hence, the statement is true and the answer is $1$.