Why is graph undefined in desmos?

Question

For the equation $x\sqrt{200-x^2}$, when I insert $\sqrt{200}$ for $x$, desmos says the output is undefined. But how can this be? The output is zero algebraically.

Answer 1

This seems like the wrong place to ask this: a desmos forum or maybe stackexchange.com itself would probably get you better answers.

As a guess though: when desmos calculates $\sqrt{200}$ it will round that to some precision (say 15 decimal places) and when it squares it again, it may use just that rounded number. In which case, the result could be slightly larger than $200$ so that it then has to try and take the square root of a negative number (e.g. $\sqrt{(200-200.00000000000191)}$) and that's what's giving you "undefined" as your answer.

But... a desmos forum would be a better place to ask; and programming forums like stackexchange may have better guesses than us mathematicians....

Answer 2

It is a rounding error issue: in this Desmos graph you see that the radicand is slightly negative: $f(\sqrt{200}) = −2.842170943×10^{−14}$. This happens due to limited precision of floating point numbers.