Question

Prove that $\frac{1}{\sqrt{3}}$ is irrational.

Answer 1

Sol:

Let us assume that $\frac{1}{\sqrt{3}}$ is rational number

$\Rightarrow \frac{1}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3}$ is also rational.

Which is only possible when $\frac{1}{3}$ and $\sqrt{3}$ both are rational. As we know that, product of two rational number is rational.

But the fact is that $\sqrt{3}$ is irrational number.

So, our assumption was wrong.

Hence, $\frac{1}{\sqrt{3}}$ is irrational.