Check whether $3\sqrt{3}$ is a rational number.

Given :

The given number is $3\sqrt{3}$
 

To do :

We have to check whether $3\sqrt{3}$ is a rational number.

Solution :

Let us assume $3\sqrt{3}$ is rational.

Hence, it can be written in the form of $\frac{a}{b}$, where a, b are co-prime, and b is not equal to 0.

$3\sqrt{3}=\frac{a}{b}$

$\sqrt{3} = \frac{a}{3b}$

Here, a, b and 3 are integers.

So, $\frac{a}{3b}$ is a rational number.

But, we know that $\sqrt{3}$ is an irrational number.

This contradicts the assumption, $3\sqrt{3}$ is rational.

Therefore, $3\sqrt{3}$ is not a rational number.

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Updated on: 10-Oct-2022

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