The value of \sqrt{Q} lies between which two consecutive integers?
N < \sqrt{Q} < N + 1
Consider the perfect squares near Q.
[What are perfect squares?]
Perfect squares are integers which can be obtained by squaring an integer.
The first 13 perfect squares are:
\qquad 1,4,9,16,25,36,49,64,81,100,121,144,169
N * N is the nearest perfect square less than Q.
(N + 1) * (N + 1) is the nearest perfect square more than Q.
So, N * N < Q < (N + 1) * (N + 1).
\sqrt{N * N} < \sqrt{Q} < \sqrt{(N + 1)*(N + 1)}
N < \sqrt{Q} < N + 1