Question

Prove that 3√5 is irrational.
​

Answer 1

$\huge\mathcal\pink{\underline{\underline{♡Añswer♡}}}$

PLZ REFER TO THE ATTACHMENT ABOVE ⬆️⬆️⬆️

FOLLOW ME ✅✅

Answer 2

Let us assume that 3√5 is a rational number.

Rational numbers are of the form p/q.

$3\sqrt{5} =\bold{{\frac{p}{q}}}$                      ( Where, p and q are co- prime and q ≠ 0)

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

Now, p/3q is a rational number.

=> √5 is a rational number.

But, this contradicts to the fact that √5 is irrational.

Hence, our assumption is wrong.

$\boxed{\boxed{\bold{Therefore, 3\sqrt{5} \ is \ an \ irrational \ number}}}}$