Lesson 2 – Simplifying Radicals

Essential Question How can properties of exponents be used to write radical expressions in useful equivalent forms?

What is a Radical? index root radicand We are familiar with taking square roots and even taking cubed roots, but you may not be as familiar with the elements of a radical. index root radicand

What is a Radical? An index in a radical tells you how many times you have to multiply the root times itself to get the radicand. When a radical is written without an index, there is an understood index of 2. For example, in 81 , 81 is the radicand, 9 is the root, and the index is 2. You have to multiply 9 by itself twice to get the radicand (9•9 = 92 = 81).

Evaluating Radicals Radicand: Index: Root: because Root: because

Evaluating Radicals with the Calculator For some of the more complex problems, you can use a calculator to help Step 1: Type in the index Step 2: Press MATH Step 3: Choose 5 Step 4: Type in the radicand

Simplifying Radicals Investigation Now you will have a chance to practice some on your own. Complete the three examples on the bottom of the page. Then move to the next side and read the introduction carefully. Your goal is to come up with methods and shortcuts to simplify the radicals. Resource Manager: Ensure everyone is on the right page Time Keeper: 10 minutes Reader/Recorder: Read each question and the introduction Spy Monitor: Check in with other groups or the key

Simplifying Radicals Find the Prime Factorization of the radicand Any sets of “n” numbers (n=index) have one representative multiplied outside Any remaining numbers no in a set are multiplied inside.

Examples In your groups, complete the remaining problems

Laura’s Entryway The floor is 3 diagonals long and 2 diagonals wide. Laura’s entry floor is made up of square tiles with 2-ft long sides The diagonal of each tile is feet in length. Find the dimensions of the floor, and then calculate the area. The floor is 3 diagonals long and 2 diagonals wide. Length: Width:

Multiplying Radicals When written in radical form, it’s only possible to write two multiplied radicals as one if the index is the same. Multiply the coefficients Multiply the radicands Simplify!

Examples In your groups, complete the remaining problems

Adding & Subtracting Radicals You can only add or subtract radicals that contain the same index and radicand. Just like you don’t change the variable expression, you won’t change the radical expression. Only add and subtract the coefficients. ALWAYS SIMPLFY THE RADICAL FIRST!

Examples In your groups, complete the remaining problems

Homework: “Lesson 2 - Simplifying Radicals Homework”