Answer:
Consider,
x = 2 √3 – 1 be a rational number.
x = 2 √3 – 1
x2 = (2 √3 – 1)2
x2 = (2 √3 )2 + (1)2 – 2(2 √3)(1)
x2 = 12 + 1 – 4 √3
x2 – 13 = – 4 √3
x – rational number, x2 – rational number
13 – x
2 – rational number
√3 is a rational number
But √3 is an irrational number, which is a contradiction.
The assumption is wrong.
Hence, (2 √3 – 1) is an irrational number.