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If $\sqrt{7}$ is an irrational number, then prove that $2\sqrt{7}$ is also an irrational number.
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Let $2\sqrt{7}$ be a rational number.
Let $2\sqrt{7}=\frac{a}{b}$ where a & b are co-prime.
$\Rightarrow \sqrt{7}=\frac{a}{2b}$
RHS is rational which contradicts the fact that $\sqrt{7}$ is irrational.
Therefore $2\sqrt{7}$ is an irrational number.
Let $2\sqrt{7}=\frac{a}{b}$ where a & b are co-prime.
$\Rightarrow \sqrt{7}=\frac{a}{2b}$
RHS is rational which contradicts the fact that $\sqrt{7}$ is irrational.
Therefore $2\sqrt{7}$ is an irrational number.