Not necessarily. In some cases, you may be able to rearrange a given formula into a quadratic without squaring both sides. It was just that in this case, that is what you had to do.
We knew that we had 2.1y=.....
And we had an equation from before which was y^2=x^2-4.
So you should be able to see that by squaring the 2.1y, and then subbing in the x^2-4 for your y^2, you can change it into a quadratic
you needed to square so you ended up with a y^2 somewhere, so that you could sub