**Q) **Prove that 2 + √3 is an irrational number, given that √3 is an irrational number.

**Ans: **Let us assume that 2 + √3 is a rational number

Let 2 + √3 = ; q ≠ 0 and p, q are integers

√3 =

Since, p and q are integers; Therefore p – 2q is an integer

Therefore, is a rational number

√3 is a rational number

But it contradicts given condition that √3 is an irrational number

**Therefore, 2 + √3 is an irrational number**