Now think of the square root of two
Suppose that it's p over q
Divide them with me
Until you can see
"No common divisor" is true

Now 2 is pp on qq
pp must be even, it's true
p's even, there's more
pp is times four
So "halve both the sides" is a clue

Half pp on qq is one
"Times qq" is easily done
qq's half pp
But even is p!
Half pp is even. Soon done:

This means q is even, I fear
And so ad absurdum, it's clear
If both q and p
Are even we see
A clear contradiction is here