Question

Show that 7root11/3 is an irrational number

Answer 1

Let us assume that 7√11/3 is a rational number.
⇒ 7√11/3 = p/q, where p ans q are integers (q ≠ 0)
⇒ √11 = 3p/7q
since p and q are integers and q ≠ 0, so 3p/7q is a rational number.
⇒ √11 is rational number.
But we know that √11 is not a rational number.
Thus we arrive at a contradiction.
Therefore, our supposition is wrong.
Hence 7√11/3 is an irrational number.  
Proved.