Question

prove that 5 + √6 is an irrational number.

Answer 1

Let us assume to the contrary that 5 +root6 is rational So, 5+root6=a/b where b is not equal to 0 Root 6 = a/b-5 Root 6 =  a-5b/b Here, a-5b/b is rational. But this contradicts with the fact that root 6 is irrational. This contradiction has arisen due to our wrong assumption that root 6 is rational. So we conclude that 5+ root 6 is irrational.