Question

Show that 5 √6 is an irrational number.

Answer 1

Let 5√6 be a rational number, which can be expressed as a / b, where b ≠ 0 ; a and b are co-primes.

       :.          5√6 = a / b

                     √6 = a / 5 b

  or,             √6 = rational

But,  √6 is an irrational number.

Thus, our assumption is wrong.

Hence, 5√6 is an irrational number.