What is the perfect square of seven?

Jun 28, 2015

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 $x = \frac{p}{q}$ is expressed in lowest terms (i.e. $p$ and $q$ have no common factor other than $1$) and $p \ge 0$, $q > 0$, then it is a perfect square if and only if both $p$ and $q$ are perfect squares.