Are all hypotenuses irrational if the shorter sides are integers?

Question

Is it sufficient to say that providing the shorter two sides of a right triangle can be expressed as integers that work out to equal the value of the hypotenuse, then the value of the hypotenuse must be irrational? For example, suppose I wish to prove that $\sqrt 5$ is irrational, if the shorter sides are 1 and 2 then the length of the hypotenuse $\sqrt 5$ must be irrational. Please tell me if I've made a mistake.

Answer 1

Hint:

take two integer numbers $m>n>0$, than: $$ a=m^2-n^2 \qquad b=2mn \qquad c=m^2+n^2 $$ are integers such that $a^2+b^2=c^2$ (which is easy to prove). These are called the Pythagorean triples.