An important and exam oriented question from real numbers in which we have given a number 2–√3 and it is already asked in previous year papers and we have to show that the given number is a irrational number.

RS Aggarwal, Class 10, chapter 1D, question no 3(ii)

Let 2 – √3 be rational.

Hence, 2 and 2 – √3 are rational.

∴ (2 – 2 + √3) = √3 = rational [∵ Difference of two rational is rational]

This contradicts the fact that √3 is irrational.

The contradiction arises by assuming 2 – √3 is rational.

Hence, 2 – √3 is irrational.