Prove that 5 - 2√3 is an irrational number.

Let,

5 - 2√3 be a rational number.

5- 2√3 = p/q [ where p and q are integer, q ≠ 0 ]

–

……(i)

We know that is a rational number.

Hence √3 is also a rational number from (i)

This contradicts our assumption.

Therefore, 5 - 2√3 is an irrational number