Question

Provide a beautiful proof of the following claim: The square of a rational number is a rational number.

Answer 1

Answer:

This fact about rational numbers is very simple. Remember $x$ is a rational number if it is a number of the form $\frac{p}{q}$ where $p,q$ are integers and $q\neq 0$. To prove this result about rational numbers  you can consider a rational number $x=\frac{p}{q}$. Then, the square of $x$ is given by

$x^{2}=x\cdot x=\frac{p}{q}\cdot \frac{p}{q}=\frac{p^2}{q^{2}}$

Note that $x^{2}$ satisfies the definition of a rational numbers.

Step-by-step explanation: