Rational root of the sum of two squares

Question

I am a freshman in highschool interested in math. Please don't judge me if the answer is either obvious or obviously doesn't exist.

Let $x$ and $y$ be rational numbers

$$x^2 + y^2 = z$$ $\sqrt z$ = rational number

Q: Are there numbers that would satisfy these equations?

Answer 1

If $x=3$ and $y=4$, then $\sqrt{z}=5$. Moreover, for any positive integers $p$ and $q$, if $x= \frac{3p}{q}$ and $y= \frac{4p}{q}$, then $\sqrt{z} = \frac{5p}{q}$.

Answer 2

You should check out Pythagorean triples...