Expression : 9√a+40√a=41√a Since equation consists of natural numbers, then 'a' must be an integer. Thus, substituting 'a' by perfect square numbers : Put a = 1 ⇒ 9√1+40√1=41√1 L.H.S. = 9+40=49≠ R.H.S. Now,putting a = 4 ⇒ 9√4+40√4=41√4 L.H.S. = 92+402=81+1600=1681 R.H.S. = 412=1681 Thus, a = 4