Question

A SUPA SHORT TUTORIAL.
Show that the product of two squares is another square.

Answer 1

This is based on the identity \(a^n \cdot b^n = (a \cdot b)^n\)
Take one integer as a, and the other integer as b.
The two perfect squares would be in the form - \(a^2\) and \(b^2\).

\( \color{Black}{\Rightarrow a^2 \cdot b^2 }\)
Simplifying:

\( \color{Black}{\Rightarrow (a \cdot b)^2}\)

Hence proved.

Answer 2

Very elegant and should be most obvious to the casual observer, but I have never thought of it.

Answer 3

Thank you sir!