Do you really want to continue using \(\sqrt{}\) in your teaching?
Do you really want to continue using \(\sqrt{}\) in your teaching? In his *Elements of Algebra*, L. Euler wrote the following.
> \(\S 200\) We may therefore entirely reject the radical signs at present made use of, and employ in their stead
> the fractional exponents which we have just explained: but as we have been long accustomed to
> those signs, and meet with them in most books of Algebra, it might be wrong to banish them entirely from
> calculations; there is, however, sufficient reason also to employ, as is now frequently done, the other method of
> notation, because it manifestly corresponds with the nature of the thing. In fact we see immediately
> that \(a^\frac12\) is the square root of \(a\), because we know that the square of \(a^\frac12\), that is to say
> \(a^\frac12\) multiplied by \(a^\frac12\) is equal to \(a^1\), or \(a\).
A lot of elementary mathematics involves converting from one form to another and back again. Sometimes these forms have important differences of use, e.g. factored form or completed square form for a quadratic. However, sometimes these equivalent forms are more customary than because it *"manifestly corresponds with the nature of the thing"* in question. I digress...