Question

Prove that $7\sqrt{5}$ is irrational.

Answer 1

Let's assume that $7\sqrt{5}$ is a rational number.
So, we can write this number as;
$7\sqrt{5}=\frac{a}{b}$
Here a and b are two co prime numbers and b$\ne$0.
$\Rightarrow$ $\sqrt{5}=\frac{a}{7b}$ ----(i)
R.H.S of equation (i) is rational number but we know that $\sqrt{5}$ is irrational number.
It is not possible.
That means our assumption is wrong.
Therefore, $7\sqrt{5}$ is an irrational number.