Simplifying Radicals

Unit 4, Lesson 2January 26th, 2015

DO Now (3 mins)Prior Knowledge Box (PKB)

Topic: Radicals Misconceptions

Write about what you know about the topic above.

StandardsN.RN The Real Number System

Extend the properties of exponents to rational exponents.

1. Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.

A.SEE Seeing Structure in Expression

Interpret the structure of expression.

1. Use the structure of an expression to identify ways to rewrite it.

Objective

Huskies will be able to relate square roots to its most simplest radical form.

Huskies will show mastery by earning a 3 out of 4 on the exit slip.

Parts of a Square Root

x3Radical Symbol

Radicand

Degree

Rules You need to know…

Rule #1

For any positive number n,

Examples

What do you notice about this rule?

*Write this in your notebook*

n ⋅ n = n

7 ⋅ 7 = 7 b ⋅ b = b 25 ⋅ 25 = 25

Rules You need to know…

Rule #2

•For any positive number n,

Examples

What do you notice about this rule?

*Write this in your notebook*

n ⋅n = n ⋅ n

3⋅3 = 3 ⋅ 3 = c ⋅c = c ⋅ c =

Did You Know…

Last One

n > 0

4 = 2− 4 = −24 = −2

Always positive

5 ⋅7 ⋅7 ⋅13the repeated product (7) comes out

7 ⋅ 5 ⋅13

ExampleSimplifying Radical Expressions.

a.) b.) c.) 18 75

NOTE: The largest perfect square factor of is

Note that the exponent mustbe even in a perfect square.

27x3 9x2

27x3

You TrySimplifying Radical Expressions.

a.) b.) c.) 45 200 75p5

Simplify Exponential Expressions (elbow partners)&

Equivalent Expressions

Take turns matching the exponential expression cards… Explain to each other how you know the cards match.

Group Activity

Using the expressions below, find the the simplified exponential expression. Use index cards to make up your group’s matching card game.

Independent Practice

Complete Lesson 2: Simplifying Radicals.

Try the Challenge Problem if you finish with extra time!

Prior Knowledge Box (PKB)

Topic: Simplifying Radicals Misconceptions

What did you think you knew about radicals but found out was

a misconception? If you didn’t have any prior knowledge, what

did you learn/review about simplifying radicals?