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7.7 Operations with Radicals

7.7 Operations with Radicals. A or of radicals can be simplified using the following rules. 1 . Simplify each in the sum. 2 . Then, combine radical terms containing the same and . sum. difference. radical. index. radicand. Simplify. 1. 2. . Simplify. 3. 4. . Simplify.

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7.7 Operations with Radicals

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  1. 7.7 Operations with Radicals

  2. A or of radicals can be simplified using the following rules. • 1. Simplify each in the sum. • 2. Then, combine radical terms containing the same and . sum difference radical index radicand

  3. Simplify. 1. 2.

  4. Simplify. 3. 4.

  5. Simplify. 5. 6.

  6. To rationalize a denominator containing two terms, we need to multiply the numerator and denominator by the of the denominator. • Conjugates of radical expressions involve the sum or difference of the same two terms. • Example: and conjugate

  7. How Does This Work?? • Multiply the conjugates below:

  8. Multiplying Conjugates *Think difference of squares!

  9. Simplify. 7. 8.

  10. We use this idea to rationalize a denominator because it gets rid of the . radical

  11. Simplify. 9.

  12. Simplify. 10.

  13. Simplify. 11.

  14. Simplify. 12.

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