Let us assume that (2√3 – 1) is a rational.
Add 1 to the above number, considering 1 is a rational number.
As we know, sum of two rational numbers is a rational.
Sum = 2√3 – 1 + 1 = 2√3
Which is only possible if 2 is rational and √3 is rational.
As we know that product of two rational numbers is rational.
But the fact is √3 is an irrational number which contradicts to our assumption.
So, (2√3 – 1) is an irrational.
