SIMPLIFYING RADICAL EXPRESSION

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

Simplify

Simplify

Part 2: Rational Exponents Rational Exponents:

Exponents that are written as fractions

Re-write in radical form

Re-write in radical form

Re-write in radical form

Re-write in radical form

Re-write in radical form

Re-write in radical form

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

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:

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: 482273122

You Try!

1) Simplify:

2)

3) Write in radical form: 4) Multiply

5) Combined: