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Simplifying Radical Expressions - Algebra Lesson

Learn how to simplify radical expressions by using the product and quotient properties of square roots. Understand the concept of a radicand and practice solving examples. Apply the Pythagorean theorem in a sports application scenario.

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Simplifying Radical Expressions - Algebra Lesson

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  1. 11.2 Radical Expressions Algebra 2.0

  2. Main Idea & Vocabulary • Our goal in this lesson will be to simplify radical expressions. • An expression that contains a radical sign ( ) is a radical expression. • The expression under a radical sign is the radicand. • A radicand may contain numbers, variables, or both. • It may contain one or more terms.

  3. Simplifying Radical Expressions • A radical expression is in simplest form if : • the radicand has no perfect squares • the radicand has no fractions • No square roots in the denominator • Remember, taking the square root means there can be positive or negative roots. • Because of this, we may need to include absolute values in our answers.

  4. Ex 1- Simplifying Radical Expressions • To simplify, use any skills to break it down.

  5. Practice 1

  6. Product Property of Square Roots • Product Property of Square Roots : For positive real numbers, √ab = √a•√b

  7. Ex 2-Using Product Property ofSquare Roots • Break down numbers to take out perfect squares • Break down exponents by making them even numbers • Divide even exponents by 2 and leave odd exponents inside radical

  8. Practice 2

  9. Quotient Property of Square Roots • Quotient Property of Square Roots: For positive real numbers,

  10. Ex 3- Using Quotient Property • Simplify the numerator • Simplify the denominator

  11. Practice 3

  12. Ex 4-Using Product & Quotient Properties Together

  13. Practice 4

  14. Ex 5-Sports Application • Pythagorean Theorem: • a2 + b2 = c2

  15. Practice 5 • Draw a picture • Decide which formula from 7th grade to use • Solve

  16. Lesson Review • What is a radical expression and a radicand? • How do we know if the radical is simplified? • What is the product property of square roots? • What is the quotient property of square roots? • When simplifying radical expressions what kind of numbers do we want to use?

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