Prove that


Prove that $\frac{2 \sqrt{3}}{5}$ is irrational.


Here we have to prove that the number $\frac{2 \sqrt{3}}{5}$ is an irrational number.

Now let us suppose that $\frac{2 \sqrt{3}}{5}=x$, where $x$ is a rational number, then

$2 \sqrt{3}=5 x$

$\Rightarrow \sqrt{3}=\frac{5 x}{2}$   ..........(1)

As $x$ is rational number, therefore form equation (1), so is $\frac{5 x}{2}$ and $\sqrt{3}$ is also a rational number which is a contradiction as $\sqrt{3}$ is an irrational number.

Therefore $\frac{2 \sqrt{3}}{5}$ is an irrational number.


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