Question

Prove that square root 3 divided by 5 is irrational

Answer 1

We have to prove that

$\frac{ \sqrt{3} }{5} \: is \: irrational$

So , we have to do this by using a contradictionary statement.

Let us consider it as a rational number, so we can write it in the form of p/q where both p and q are co prime Integers.

So ,

$\frac{ \sqrt{3} }{5} = \frac{p}{q}$

$\sqrt{3} = \frac{5p}{q}$

As 5p/q is a rational number so √3 is also a rational number. But it can't be possible because √3 is an irrational number.