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Mastering the Product Rule for Radicals

Learn how to multiply and simplify radical expressions using the product rule. Discover patterns in perfect squares, cubes, and fourth powers. Practice simplifying radicals with examples and recall rules for even and odd exponents.

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Mastering the Product Rule for Radicals

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  1. Math 71B 7.3 – Multiplying and Simplifying Radical Expressions

  2. Product Rule for Radicals (Disclaimer: Only works when are real #s. Some restrictions apply. See stores for details.)

  3. Product Rule for Radicals Ex 1.Multiply:

  4. Product Rule for Radicals Ex 1.Multiply:

  5. Product Rule for Radicals Ex 1.Multiply:

  6. Simplifying Radicals 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, … are ___________________(squares of integers) 8, 27, 64, 125, 216, 343, … are ______________ 16, 81, 256, 625, … are____________________

  7. Simplifying Radicals 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, … are ___________________(squares of integers) 8, 27, 64, 125, 216, 343, … are ______________ 16, 81, 256, 625, … are____________________ perfect squares

  8. Simplifying Radicals 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, … are ___________________(squares of integers) 8, 27, 64, 125, 216, 343, … are ______________ 16, 81, 256, 625, … are____________________ perfect squares perfect cubes

  9. Simplifying Radicals 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, … are ___________________(squares of integers) 8, 27, 64, 125, 216, 343, … are ______________ 16, 81, 256, 625, … are____________________ perfect squares perfect cubes perfect fourth powers

  10. Simplifying Radicals Ex 2.Simplify:

  11. Simplifying Radicals Recall: If is even, . If is odd, . Note: If is nonnegative, then the first rule becomes _____.

  12. Simplifying Radicals Recall: If is even, . If is odd, . Note: If is nonnegative, then the first rule becomes _____.

  13. Simplifying Radicals Ex 3.Simplify (assume that all variables are positive real numbers).

  14. Simplifying Radicals Ex 4.Multiply and simplify (assume that all variables are positive real numbers):

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