P: grass is green or Q: 3 is the square root of 10 (P ∨ Q)

P v Q is a disjunction, which is true whenever P or Q is true or both are true. P v Q is false only when P and Q are both false.

You know that Q is false, because 3 is not the square root of 10, so the only possibility for P v Q be true is that P is true.

If that is the case, you have this relation:

T F - - - > T

which means True and False imply True