Prove that the following number is irrational: $7 \sqrt{5}$

(N/A) Let us assume,to the contrary,that $7 \sqrt{5}$ is a rational number.
Then,there exist coprime integers $a$ and $b$ $(b \neq 0)$ such that $7 \sqrt{5} = \frac{a}{b}$.
Rearranging the equation,we get $\sqrt{5} = \frac{a}{7b}$.
Since $a$ and $b$ are integers,$\frac{a}{7b}$ is a rational number.
This implies that $\sqrt{5}$ is a rational number.
However,this contradicts the fact that $\sqrt{5}$ is an irrational number.
This contradiction has arisen because of our incorrect assumption that $7 \sqrt{5}$ is rational.
Therefore,we conclude that $7 \sqrt{5}$ is an irrational number.