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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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