Question

proove that 2√3- 5 is an irrational number​

Answer 1

let us assume that 2√3-5 is rational

so it can be expressed as 2√3-5=a/b (where a and b are coprimes)

2√3-5=a/b

√3=a/2b+5

Here, a/2b+5 is rational. So,√3 is also rational.

But this contradicts the fact that √3 is irrational.

This contradiction has arisen because of our incorrect assumption that 2√3-5 is rational.

Therefore, we can conclude that 2√3-5 is irrational.