Prove that is an irrational number.

Rationalizing the fraction we get,

x = 2 - √3

Now Let x = 2 - √3 be a rational number

A rational number can be written in the form of p/q where p, q are integers.

Now As p and q are rational numbers, should also be a rational number. But this is not the case.

Hence, the statements contradict. Thus, is an irrational Number.