11-2 Operations with Radical Expressions Objectives SWBAT: Add and subtract radical expressions Multiply radical expressions

Adding and Subtracting Radical Expressions Adding and subtracting radicals is very similar to adding and subtracting monomials. Remember, to add or subtract monomials, you need the same variables and same exponents on those variables (like terms). To add or subtract radical expressions, you need the same radicand and same index (like radical expressions) If the terms have the same radicand and same index, you add/subtract the terms on the outside of the radical expression, and keep the index and radicand. Note: Just because radicals appear to be unlike, doesn’t necessarily mean they are unlike. You need to see if you can simplify the radicand first. Often times, simplifying the radicand will reveal like radicals.

Example 1: Simplify each expression. 1) 2) 3) 4) 5) 6)

7) 8) 9) 10)

Try these. 11) 12)

Multiplying Radical Expressions When multiplying radical expressions, the terms on the outside of the radicals get multiplied, and the radicands get multiplied. Then simplify, if possible. If you choose, you can simplify the radical expressions first (if possible), and then multiply.

Example 2: Find each product. 1) 2) 3) 4) 5) 6)

7) 8) 9) 10)

Try these. 11) 12) 13) 14)