Question

show that 3√3 is an irrational

Answer 1

Hey mate..
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Let us assume to the contrary that
$3 \sqrt{3}$
is a rational number.

So,

$3 \sqrt{3} = \frac{p}{q}$ ( where p,q are co-prime numbers and q is not equal to zero )

$= > \sqrt{3} = \frac{p}{3q}$

Since, p and q are integers, $\frac{p}{3q}$ is a rational number .

So,
$\sqrt{3}$ is a rational number

But it is impossible since,
$3 \sqrt{3}$
is irrational .

So, We came to conclusion that , $3 \sqrt{3}$ is an irrational number.

( Hence, Proved )

Hope it helps !!