Objective: Add, subtract and multiplying radical expressions; re-write rational exponents in radical form. Essential Question: What rules apply for adding, subtracting and multiplying radicals? What are rational exponents?

Parts of a radical expression:

Part 1: How to Simplify  1. Make a factor tree  2. Circle groups of  Two (square root)  Three (cube root)  Four (fourth root)  Move one number from each group to the outside

Simplify

Part 2: Rational Exponents  Rational Exponents:  Exponents that are written as fractions

Re-write in radical form

Part 3: Multiplying  You cannot multiply radicals if the indexes are different  Multiply the coefficients and radicands  Simplify answer by making a factor tree

Multiply & Simplify

Part 4: Adding & Subtracting  You cannot add/subtract radicals if the indexes or radicands are different  Simplify by making a factor tree first  Add coefficients, keep the radicand the same

Combined expressions:

You Try! 1) Simplify: 2) 3) Write in radical form: 4) Multiply 5) Combined:

You Try! 1) Simplify: 2) 3) Write in radical form: 4) Multiply 5) Combined:

You Try! 1) Simplify: 2) 3) Write in radical form: 4) Multiply 5) Combined:

You Try! 1) Simplify: 2) 3) Write in radical form: 4) Multiply 5) Combined:

You Try! 1) Simplify: 2) 3) Write in radical form: 4) Multiply 5) Combined:

You Try! 1) Simplify: 2) 3) Write in radical form: 4) Multiply 5) Combined: