Any number such
as 64 = 8^{2} which is equal to the square of a whole number, is called
a perfect square. The first 8 square numbers are.

1 = 1^{2}, 4 = 2^{2},
9 = 3^{2}, 16 = 4^{2}, 25 = 5^{2}, 36 = 6^{2}, 49 = 7^{2},
64 = 8^{2}, 11^{2} = 121,

12^{2} = 144, 13^{2} = 169, 14^{2} = 196, 15^{2} = 225, 16^{2} = 256,
17^{2} = 289, 18^{2} = 324,

19^{2} = 361, 20^{2} = 400

All such numbers
can be represented by a square array of dots. Squares of even numbers
are even, since (2n)^{2} = 4n^{2}.

Squares of odd
numbers are odd, since (2n + 1)^{2} = 4(n^{2} + n) + 1

It follows that
square roots of even square numbers are even, and square roots of
odd square numbers are odd.