N1=2, N2=3, N3=5, N4=6 , ... , Ni=i-th non square integer.Please help me with a solution to the following problem,I've been trying this for somedays but is unable to approach it in any way...

It is found that for some integer m, m^2< Nn <(m+1)^2

Prove that m= [√n + (1/2)] where [x]=Greatest Integer Function.