If you can't think of that number, you can break down Q into
its prime factorization and look for equal groups of numbers.
Let's draw a factor tree.
So the prime factorization of Q is PRIMES.join( "\\times " ).
\Large{\sqrt{Q} = \text{?}}
N
\sqrt{Q} is the number that, when
multiplied by itself, equals Q.
We're looking for \sqrt{Q}, so we want to split the prime factors into two identical groups.
We only have two prime factors, and we want to split them into two groups, so this is easy.
Q = PRIMES.join( "\\times " ), so N^2 = Q.
Notice that we can rearrange the factors like so:
Q = PRIMES.join(" \\times ") = \left(F_N.join( "\\times " )\right) \times \left(F_N.join(" \\times ")\right)
So \left(F_N.join( "\\times " )\right)^2 = N^2 = Q.
So N^2 = Q.
So \sqrt{Q} is N.