Question

Question #09aeb

Answer 1

There is no one answer. It always meant the square of something in some chosen set, but the chosen set varies.

Explanation:

Many use "perfect square" to mean the square of an integer.
E.g. `25` is the square of `5`, so `25` is a perfect square.

Many also use it to mean the square of an integer or the square on a polynomial with integer coefficients.
E.g. `x^2+6x+9` is the square of `x+3`, so `x^2+6x+9` perfect square. (Sometimes "a perfect square polynomial.)

Others replace "integer" in the preceding with "rational number".
E.g. `16/9` is the square of `4/3`, so `16/9` is a perfect square.
E.g. `25/49x^4` is the square of `5/7x^2`, so `25/49x^4` is a perfect square.

There are other uses as well.