Is #0.25# a perfect square?
If you notice, both the numerator
According to the Wikipedia article on square numbers, "the ratio of any two square integers is a square".
Yes, but it's worth a few remarks...
Perfect square integers
If we are talking about integers, then we tend to be fairly clear what we mean by a perfect square, namely:
#0, 1, 4, 9, 16, 25, 36, 49,...#
That is - a perfect square is a number which is the square of an integer.
Perfect square rationals
When a number such as
#0.25 = 1/4 = 1/2^2 = (1/2)^2 = 0.5^2#
So it does qualify as being called a perfect square.
In general we find that the only rational numbers which are squares of rational numbers can always be expressed in the form
One step beyond...
It is not the square of a rational number, so you would not normally count it as such, but consider the following:
You will find that
In greater generality, any Complex number is - in a sense - a perfect square in that it is the square of a Complex number.
Concepts like "perfect square" are sensitive to context. In the given example of