Parametric equations question

T is also x/3, from the first equation. And complicated equation. You still can do that.

T is being raised to the power of 3 though, I can’t simply divide by 3...

I’m finding a Cartesian equation for the parametric equations of

X=t^3, y=2(t^2)
Normally I would just eliminate t from x and sub into y but I remember my teacher saying never to take square/cube roots when doing parametrics as you’d lose solutions

What would I do in this case?

There's nothing wrong with taking roots as long as you're consistent. Here, taking a square root will introduce you to $\pm \sqrt{\frac{y}{2}}$ but if you consider the fact that any odd root doesn't introduce this $\pm$ business, then taking the cube root of $x$ is the way to go to get $t$

So my answer is simply 2x^2/3 ?

Yes.