Lesson 11-1

Simplifying Radical Expressions

5-Minute Check on Chapter 25-Minute Check on Chapter 25-Minute Check on Chapter 25-Minute Check on Chapter 2 Transparency 3-1

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1. Evaluate 42 - |x - 7| if x = -3

2. Find 4.1 (-0.5)

Simplify each expression

3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9)

5. A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is not green?

6. Which of the following is a true statementStandardized Test Practice:

A CB D8/4 < 4/8 -4/8 < -8/4 -4/8 > -8/4 -4/8 > 4/8

Objectives

• xxxxxx

Vocabulary

• Radical Expression –

• Radicand –

• Rationalizing the denominator –

• Conjugate –

Square Root Properties

• Product Property

– English: The square root of a product is equal to the product of its square roots

– Symbols:

• Quotient Property

– English: The square root of a quotient is equal to the quotient of its square roots

– Symbols:

√ab = √a √b

a √a --- = ---- b √b

Example 1

A. Simplify

Prime factorization of 52

Product Property of Square Roots

Answer: Simplify.

B. Simplify

Product Property of Square Roots

Simplify.

Prime factorization of 72

Answer: Simplify.

Example 2

Find

Product Property

Answer: Simplify.

Product Property

Example 3

Simplify

Prime factorization

Product Property

Simplify.

The absolute value of ensures a nonnegative result.

Answer:

Example 4a

A. Simplify

Answer: Simplify.

Product Property of Square Roots

Multiply by .

Example 4b

B. Simplify

Prime factorization

Multiply by

Answer: Product Property of Square Roots

Example 4c

Product Property of Square Roots

Prime factorization

C. Simplify

Multiply by

Answer: Cancel out 2 from top and bottom

Example 5

Simplify

Simplify.Answer:

Summary & Homework

• Summary:A radical expression is in simplest form when:– no radicands have perfect square factors other

than 1, – no radicands contain fractions, and– no radicals appear in the denominator of a fraction

• Homework: – pg