randRange( 2, 11 ) randRange( N * N + 1, (N + 1) * (N + 1) - 1 )

The value of `\sqrt{Q}` lies between which two consecutive integers?

Integers that appear in order when counting, for example 2 and 3.

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`