Simplifying multiplied radicals is pretty simple, being barely different from the simplifications that we've already done. We use the fact that the product of two radicals is the same as the radical of the product, and vice versa. Write as the product of two radicals: Because 6 factors as 2 × 3, I can split this one radical into a product of two radicals by using the factorization. (Yes, I ...

I can only combine the "like" radicals. The first and last terms contain the square root of three, so they can be combined; the middle term contains the square root of five, so it cannot be combined with the others. So, in this case, I'll end up with two terms in my answer.

(Okay, technically they're integers, but the point is that the terms do not include any radicals.) I multiplied two radical binomials together and got an answer that contained no radicals. You may also have noticed that the two "binomials" were the same except for the sign in the middle: one had a "plus" and the other had a "minus".

In this case, they've given me a product of fourth roots. I can convert the product of radicals into the radical of a product. Then I can simplify. Adding Higher-Index Roots. Simplify: The terms in this expression are both cube roots, but I can combine them only if they're the cube roots of the same value. Right now, they aren't. So I'll simplify the radicals first, and then see if I can go ...