Splash Screen Unit 6 Exponents and Radicals

Splash Screen Essential Question: How do you simplify radical expressions?

In this lesson, work will be done with radicals, specifically square root radicals, such as _____ or _____.

What is a RADICAL? If n is a positive integer that is greater than 1 and a is a real number then, where n is called the index, a is called the radicand, and the symbol √ is called the radical.

1 2 = = = = = = = = = = = = = = = 225 Perfect Squares Know these!

Square Root - easy definition A number that when multiplied by itself equals a given number. Root A number that, when multiplied by itself some number of times, equals a given number.

Then/Now You simplified radicals. Simplify radical expressions by using the Product Property of Square Roots. Simplify radical expressions by using the Quotient Property of Square Roots. EQ: How do simplify radical expressions?

Vocabulary radical expression rationalizing the denominator

A radicand is in simplest form if the following 3 conditions are true. No radicands have _________ square factors other than 1. perfect #1

A radicand is in simplest form if the following 3 conditions are true. No radicands contain ______________. fractions #2

A radicand is in simplest form if the following 3 conditions are true. No radicals appear in the denominator of a ______________. fraction #3

Concept 1

A radicand is in simplest form if the following 3 conditions are true. No radicands have _________ square factors other than 1. perfect #1

Example 1 Simplify Square Roots

Example 1 Simplify Square Roots

Example 1 Simplify Square Roots

Example 1 Simplify Square Roots

Example 1 Simplify Square Roots

Example 1 Simplify Square Roots

Example 1 Simplify Square Roots

Example 1 Simplify Square Roots

Example 1 A. B. C.15 D.

Concept 1 A. B. C. D. Do these examples on the practice worksheet.

Example 2 Multiply Square Roots

Example 2 A. B. C. D.35

Concept 1 E. F. G. H. Do these examples on the practice worksheet.

Example 3 Simplify a Square Root with Variables Prime factorization Product Property Simplify. Answer:

Example 3 A. B. C. D.

I. Do these examples on the practice worksheet.

J. Do these examples on the practice worksheet.

K. Do these examples on the practice worksheet.

L. Do these examples on the practice worksheet.

End of the Lesson Assignment: Do #1 to #34 on the Practice Worksheet

Concept 2

A radicand is in simplest form if the following 3 conditions are true. No radicands contain ______________. fractions #2

A radicand is in simplest form if the following 3 conditions are true. No radicals appear in the denominator of a ______________. fraction #3

Concept 2 Multiplying by 1 does not change it’s value. Rationalizing the Denominator

Multiplying by 1 does not change it’s value. Rationalizing the Denominator

Multiplying by 1 does not change it’s value. Rationalizing the Denominator

Example 4 A. B. C. D.

Example 4 Which expression is equivalent to ? AC BDAC BD

M. N. Do these examples on the practice worksheet.

O. P. Do these examples on the practice worksheet.

End of the Lesson Assignment: Complete the Practice Worksheet