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Simplifying Radical Expressions

Simplifying Radical Expressions. For any numbers a and b where and , . Product Property of Radicals. Product Property of Radicals Examples. Examples :. Examples :. For any numbers a and b where and , . Quotient Property of Radicals. Examples :. Examples :.

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Simplifying Radical Expressions

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  1. Simplifying Radical Expressions

  2. For any numbers a and b where and , Product Property of Radicals

  3. Product Property of RadicalsExamples

  4. Examples:

  5. Examples:

  6. For any numbers a and b where and , Quotient Property of Radicals

  7. Examples:

  8. Examples:

  9. Rationalizing the denominator Rationalizing the denominator means to remove any radicals from the denominator. Ex: Simplify

  10. Simplest Radical Form • No perfect nth power factors other than 1. • No fractions in the radicand. • No radicals in the denominator.

  11. Examples:

  12. Examples:

  13. Adding radicals We can only combine terms with radicals if we have like radicals Reverse of the Distributive Property

  14. Examples:

  15. Examples:

  16. Multiplying radicals - Distributive Property

  17. O F L I Multiplying radicals - FOIL

  18. O F L I Examples:

  19. O F L I Examples:

  20. Binomials of the form where a, b, c, d are rational numbers. Conjugates

  21. The product of conjugates is a rational number. Therefore, we can rationalize denominator of a fraction by multiplying by its conjugate.

  22. Examples:

  23. Examples:

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