Question

What is the perfect square of seven?

Answer 1

The square of seven is `49`. We say that `49` is a perfect square because it is the square of a whole number `7`.

Explanation:

If `n` is a whole number then we call it a perfect square if there is some whole `m` such that `n = m^2`.

If `x` is a rational number, then we call it a perfect square if there is some rational number `w` such that `x = w^2`. In fact if `x=p/q` is expressed in lowest terms (i.e. `p` and `q` have no common factor other than `1`) and `p >= 0`, `q > 0`, then it is a perfect square if and only if both `p` and `q` are perfect squares.