Prove that
         (a) 2 + is not a rational number and 
         (b)  is not a rational number.              

If possible, let 2 + = a , where a is rational.
        Then, (2 + ) = a
                   7 + 4 = a
                          =-------(i)
Now , a is rational ⇒    is rational.
is rational [from (i)]
This is a contradiction.
Hence, 2 + is not a rational number.
(b) If possible, let = p/q , where p and q are integers, having no common factors and q ≠ 0.
Then, () = (p/q)
⇒ 7q = p------(i)
⇒ p is a multiple of 7
⇒ p is multiple of 7.
Let p = 7m, where m is an integer.
Then, p = 343 m ------(ii)
  ⇒ 7q = 343 m [from (i) and (ii)]
   ⇒ q = 49 m
⇒ q is a multiple of 7.
⇒ q is a multiple of 7.
Thus, p and q are both multiples of 7, or 7 is a factor of p and q.
This contradicts our assumption that p and q have no common factors.
Hence is not a rational number.