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Radical Expressions: Simplification and Multiplication Tips

Learn how to multiply and simplify radical expressions, rationalize denominators, and apply various product properties of square roots for simplification. Practice examples included.

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Radical Expressions: Simplification and Multiplication Tips

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  1. Warm Up • Simplify each expression. • 1. • 2. • 3. • 4.

  2. Objectives Multiply and divide radical expressions. Rationalize denominators.

  3. Directions: Multiply. Write the product in simplest form.

  4. Example 1 Product Property of Square Roots. Multiply the factors in the radicand. Factor 16 using a perfect-square factor. Product Property of Square Roots Simplify.

  5. Example 2 Expand the expression. Commutative Property of Multiplication. Product Property of Square Roots. Simplify the radicand. Simplify the Square Root. Multiply.

  6. Example 3 Factor 4 using a perfect-square factor. Product Property of Square Roots. Take the square root.. Simplify.

  7. Example 4 Product Property of Square Roots. Multiply the factors in the radicand. Factor 25 using a perfect-square factor. Product Property of Square Roots Simplify.

  8. Example 5 Expand the expression. Commutative Property of Multiplication. Product Property of Square Roots. Simplify the radicand. Simplify the Square Root. Multiply.

  9. Example 6 Factor 14 using a perfect-square factor. Product Property of Square Roots. Take the square root. Simplify.

  10. Distribute Example 7 Product Property of Square Roots. Multiply the factors in the second radicand. Factor 24 using a perfect-square factor. Product Property of Square Roots. Simplify.

  11. Distribute Example 8 Product Property of Square Roots. Simplify the radicands. Simplify.

  12. Distribute Example 9 Product Property of Square Roots. Multiply the factors in the first radicand. Factor 48 using a perfect-square factor. Product Property of Square Roots. Simplify.

  13. Distribute Example 10 Product Property of Square Roots. Simplify the radicand. Simplify.

  14. Distribute Example 11 Product Property of Square Roots. Simplify the radicand. Simplify.

  15. Distribute Example 12 Product Property of Square Roots. Simplify the radicand. Simplify.

  16. Lesson Summary Multiply. Write each product in simplest form. 1. 2. 3. 4. 5. 6.

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