In this lesson, we’re going to expand expressions involving surds. And we’re going to use our rules from algebra to help with our expansions.

Can you see what will happen when we have root two outside of root seven minus root three? Yes. We multiply each term in the brackets by the square root of two. That gives root two times root seven minus root two times root three.

We know the square root of two times root seven can be written as the square root of two times seven or root 14. And minus root two times root three can be written as minus root six.

Can you see these new values are unlike terms and so we can’t do anything more with this particular expression?