Any number such
as 64 = 82 which is equal to the square of a whole number, is called
a perfect square. The first 8 square numbers are.
1 = 12, 4 = 22,
9 = 32, 16 = 42, 25 = 52, 36 = 62, 49 = 72,
64 = 82, 112 = 121,
122 = 144, 132 = 169, 142 = 196, 152 = 225, 162 = 256,
172 = 289, 182 = 324,
192 = 361, 202 = 400
All such numbers
can be represented by a square array of dots. Squares of even numbers
are even, since (2n)2 = 4n2.
Squares of odd
numbers are odd, since (2n + 1)2 = 4(n2 + n) + 1
It follows that
square roots of even square numbers are even, and square roots of
odd square numbers are odd.
