Homer’s Theorem

I learn from this,
"The square roots of the two shorter sides' sum 
"Of a Right Triangle
"Is equal to the square root of the longer,"
In purely logical form...
The equality breaks down
And Algebra ceases to function.

Take the Pythagorean Theorem.
If one square roots the C variable, and square roots it again,
The same must be done to the opposite side.
Creating Homer's Theorem.
Frighteningly, I see the problem with modern mathematics,
In that when we are taught pure deduction,
We are never taught the practical applications.
Thus, Algebra breaks down where there is nothing 
Extant to base it on... or at least it can, as proven by Homer's Theorem.

Coincidentally, the Pythagorean Theorem also 
Breaks algebra in itself, that it wouldn't exist
If one could merely square root both sides of an equation.
Then, necessarily, A+B=C is the same as A^2+B^2=C^2
If this axiom holds true.
Which, if it did, well, then there'd be no discovery.

Of course, I'm probably not the first to have trifled with this.
So, I'm confident there is an explanation.