how many integral values of n are possible for (\sqrt{n}+\sqrt{n+2013}) to be rational?

Question

how many integral values of n are possible for (\sqrt{n}+\sqrt{n+2013})  to be rational?

anonymous · Answer

it is $$\sqrt{n}+\sqrt{n+2013}$$  !!

anonymous · Answer

n could be anything greater than zero I think...

anonymous · Answer

what values ??

aravindg · Answer

for a number to be rational we should be able to express it in form a/b  where a and b are  2 integers , clearly $$x \ge 0 $$ for square root to operate

anonymous · Answer

Yes, what Aravind said.

aravindg · Answer

its *n sorry

aravindg · Answer

now both  $\sqrt{n}$ and  $\sqrt{n+2}$ are irrational numbers ...but we can get a rational numbers for some particular values of n 
 
clearly n not equal to 0 

now  see we which is the next perfect square after 2013 ?

aravindg · Answer

*n+2013  sorry for typo

anonymous · Answer

next perfect square after 2013 is $$45^2$$=2025?

anonymous · Answer

then what?

anonymous · Answer

u der?

aravindg · Answer

pls wait a min

anonymous · Answer

ok!

aravindg · Answer

i was trying to get to the solution using trial and error method  ...finding a suitable square number that satisfies our situation

anonymous · Answer

so what would be those numbers?

anonymous · Answer

by hit and trial n can  be $$196$$
and what else?

anonymous · Answer

also it would be very long !

aravindg · Answer

i understand ... i am trying an alternate solution ...will post if I succeed ..thanks for patience I got guests at my house sorry for delay