Question

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

${\left(\frac{\sqrt{7}}{6\sqrt{2}}\right)}^2$.

Answer 1

Rational numbers are those numbers which can be expressed in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$
Now, ${\left(\frac{\sqrt{7}}{6\sqrt{2}}\right)}^2=\frac{7}{36\times 2}=\frac{7}{72}$, which is of the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$.
That is, ${\left(\frac{\sqrt{7}}{6\sqrt{2}}\right)}^2$ is a rational number.

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