Is it safe to remove this tree root?

Hi everyone,

We're trying to sort out the front garden and, after some digging, found a tree root (see picture) that runs under the concrete and potentially under the house.

We don't want to harm the tree. Given this, is it safe to remove this root? Does a tree have multiple roots and perhaps wouldn't miss this one (I'm very new to this), or would it cause damage? Is burying the root deeper a better option?