Question

prove that 3√5 is ir rational​

Answer 1

S O L U T I O N :

Let we the 3√5 is a rational number.

So, we know that p and q are two  integers and q ≠ 0.

Now;

$\longrightarrow\sf{3\sqrt{5} =\dfrac{p}{q} }\\\\\longrightarrow\sf{3q\sqrt{5} =p}\\\\\longrightarrow\sf{\sqrt{5} =\dfrac{p}{3q} }$

∴ p/3q is a rational number , √5 is an irrational number.

So, rational number can't equal to an irrational number.

Hence, our contradiction is wrong.

Thus;

3√5 is an irrational number.