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Simplifying Radical Expressions: Perfect Squares and Prime Factorization

This lesson focuses on simplifying radical expressions, with an emphasis on perfect squares and prime factorization. Students will begin with a warm-up activity to identify perfect squares from given sets and then write numbers as products of prime numbers. The objective is to help students understand radical expressions and their properties, including the importance of nonnegative roots. The lesson includes examples and the Product Property of Square Roots, guiding students through the process of simplification while ensuring clarity on variables representing nonnegative numbers.

brielle-macdonald
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Simplifying Radical Expressions: Perfect Squares and Prime Factorization

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  1. 11-6 Radical Expressions Warm Up Lesson Presentation Lesson Quiz Holt Algebra 1

  2. Warm Up • Identify the perfect square in each set. • 1. 45 81 27 111 • 2. 156 99 8 25 • 3. 256 84 12 1000 • 4. 35 216 196 72 81 25 256 196

  3. Warm Up Continued Write each number as a product of prime numbers. 5. 36 6. 64 7. 196 8. 24

  4. Objective Simplify radical expressions.

  5. Vocabulary radical expression radicand

  6. Remember that positive numbers have two square roots, one positive and one negative. However, indicates a nonnegative square root. When you simplify, be sure that your answer is not negative. To simplify you should write because you do not know whether x is positive or negative.

  7. Check It Out! Example 1 Simplify each expression. a. b.

  8. Example 2A: Using the Product Property of Square Roots Simplify. All variables represent nonnegative numbers. Factor the radicand using perfect squares. Product Property of Square Roots. Simplify.

  9. Check It Out! Example 2a Simplify. All variables represent nonnegative numbers. Factor the radicand using perfect squares. Product Property of Square Roots. Simplify.

  10. Check It Out! Example 2a Simplify. All variables represent nonnegative numbers. Factor the radicand using perfect squares. Product Property of Square Roots. Simplify.

  11. Check It Out! Example 2a Simplify. All variables represent nonnegative numbers. Factor the radicand using perfect squares. Product Property of Square Roots. Simplify.

  12. Check It Out! Example 2a Simplify. All variables represent nonnegative numbers. Factor the radicand using perfect squares. Product Property of Square Roots. Simplify.

  13. Check It Out! Example 2a Simplify. All variables represent nonnegative numbers. Factor the radicand using perfect squares. Product Property of Square Roots. Simplify.

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