One reason you learned to simplify radicals is to be able to combine them. Radicals are called similar if they have the same index and same radicand, such as 4·∛(xy) and 7·∛(xy). You add and subtract radicals by combining similar radicals.

Add and Subtract Radicals

Multiply and Divide Radicals

To multiply two or more radicals together, make sure that the index of each factor match. When the indices match, the process is relatively easy: write all the factors underneath one common radical, then simplify the radicand. On the contrary, when they’re different, each factor needs to be algebraically manipulated to match before you can multiply. Both technique is fully demonstrated in the video below.

To be successful at dividing radicals, you’ll need to remember an important skill you learned earlier in this unit regarding rationalizing the denominator. In addition, you need to remember how to divide a polynomial by a monomial; that lessons can be found here (video link here). A visual demonstration is provided below:

In case you’re asked to divide two binomials, another technique you learned earlier in this course may come in handy. Remember when you learned how to simplify fraction containing complex numbers, you multiplied and divided the quotient by the conjugate of the denominator. Watch the video below to see how it can be applied here: