Question

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

${(\sqrt{3}-\sqrt{2})}^2$.

Answer 1

$(\sqrt{3}-\sqrt{2}{)}^2=3-2\sqrt{6}+2........$ Use identity, $(a-b{)}^2=a^2-2ab+b^2$

As $\sqrt{6}$ is an irrational number, (which is not in the form of $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$,

therefore given number is an irrational number.

Hence, the statement is false and the answer is $0$.