Question

show that 2-3√5 is irrational

Answer 1

Hello friend

Here goes your answer

Let us assume 2-3√5 to be a rational number

A rational number is a one which can be expressed in the form p/q

So 2-3√5=p/q

For some integers p,q

3√5=2-(p/q)

3√5=2q-p/q

√5=2q-p/3q

As p,q are integers the RHS will be a rational number

So LHS also needs.to be a rational number

But this contradicts the fact that√5 is irrational. This contradiction has arisen due to our false assumption.

Therefore 2-3√5 is irrational