Let (2√3−1) be a rational number.
A rational number can be written in the form of pq where p,q are integers.
2√3−1=pq
2√3=pq+1
2√3=p+qq
√3=p+q2q
p,q are integers then p+q2q is a rational number.
Then,√3 is also a rational number.
But this contradicts the fact that √3 is an irrational number.
Therefore, our supposition is false.
So,2√3−1 is an irrational number.