- Topics At a Glance
- Squares
- Simplification of Radical Terms
- Multiplication
- Division
- Radicals in the Denominator
**Radical Arithmetic**- Addition and Subtraction
**Multiplication**- Division
- Quadratic Equations
- Taking Square Roots
- Completing the Square
- Quadratic Formula
- Solving Radical Equations
- The Pythagorean Theorem
- Word Problems
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem
- Yes, This Really Is a Square

Multiplication of radical expressions is similar to multiplication of polynomials. Remember what a gas that was? Now we can experience that thrill ride all over again, and you don't even need to wait in an incredibly long line first.

When multiplying radical expressions, we give the answer in simplified form. Multiplying two monomial (1-term) radical expressions is the same thing as simplifying a radical term.

Multiply .

We multiply the radicands to find .

Then, we simplify our answer to .

Multiply

We distribute the and simplify the resulting terms:

Since these simplified terms have different radicands, there are no like terms to combine, so we're done. If you absolutely need a combining fix, we suggest experimenting with your little sister's poster paints. Hint: Yellow and blue make green.

To find the product of two binomial (2-term) radical expressions, we use FOIL. We're sure you've managed to preserve your memory of how to do this; good thing you wrapped it in FOIL.

Multiply .

The first thing we do is simplify each radical term, if possible. We can replace with 2, and now the problem is

.

Now we use FOIL. First, outside, inside, last. It's all coming back to you now, right? Don't give us that look, everyone loves Celine.

Anyway, we start by multiplying the first terms:

,

which gives us

.

We multiply the outside terms:

,

which gives us

.

We multiply the inside terms:

which gives us

.

Finally, we multiply the last terms:

,

which gives us

.

Adding together all of our cute little products yields

.

Since the radicals have different radicandsâ€”one might even say "radically different radicands," which we willâ€”this is as simplified as the answer gets. Rad.

Example 1

Multiply . |

Example 2

Multiply . |

Example 3

Multiply . |

Exercise 1

Multiply, remembering to simplify: .

Exercise 2

Multiply, remembering to simplify: .

Exercise 3

Multiply, remembering to simplify: .

Exercise 4

Multiply, remembering to simplify: .

Exercise 5

Multiply, remembering to simplify: .

Exercise 6

Multiply, remembering to simplify: .

Exercise 7

Multiply, remembering to simplify: .

Exercise 8

Multiply, remembering to simplify: .

Exercise 9

Multiply, remembering to simplify: .

Exercise 10

Multiply, remembering to simplify: .