**Q) **Prove that 6 – √7 is an irrational number, given that √7 is an irrational number.

**Ans: **Let us assume that 6 – √7 is a rational number

Let 6 – √7 = ; q ≠ 0 and p, q are integers

√7 =

Since, p and q are integers; Therefore 6q – p is an integer

Therefore, is a rational number

√7 is a rational number

But it contradicts given condition that √7 is an irrational number

**Therefore, 6 – √7 is an irrational number………… Hence Proved !**