I just want to double check my work as I'm not entirely sure in my answers. If I got anything wrong please do tell me!
a) The equation $x^3 = 27$ has a natural number solution.
$$\exists x\in\mathbb{N},\ (x^3 = 27)$$
b) $0$ is less than or equal to every natural number.
$$\exists x\in\mathbb{N},\ (x \geq 0)$$
c) Every real number is rational.
$$\exists x\in\mathbb{R},\ (x\in\mathbb{Q})$$
Your answer to (a) is correct, but the other two are not.
Your answer to (b) says in plain English that there is at least one natural number that is greater than or equal to $0$. You need the other quantifier: $\forall x\in\Bbb N(0\le x)$ says that $0$ is less than or equal to every natural number.
Your answer to (c) says that there is at least one real number that is rational. Here again you want the other quantifier: $\forall x\in\Bbb R(x\in\Bbb Q)$ says that every real number is rational.
Remember, you can always read $\forall x$ as for all $x$ such that or for each $x$ such that, and you can always read $\exists x$ as there is at least one $x$ such that.