Question

show that 5-2√3 is irrational no.

Answer 1

Hello friend

Here goes your answer

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

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

So 5-2√3=p/q

For some integers p,q

2√3=5-(p/q)

2√3=5q-p/q

√3=5q-p/2q

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√3 is irrational. This contradiction has arisen due to our false assumption.

Therefore 3-2√5 is irrational