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7.1 and 7.2 Simplifying/Multiplying/Dividing Radical expressions

7.1 and 7.2 Simplifying/Multiplying/Dividing Radical expressions. Nth Roots. For any real number a and b, and any positive integer n, if a n = b , then a is the n th root of b. Real Number Examples :. Find the roots: Square Root of 4 Square Root of - 4

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7.1 and 7.2 Simplifying/Multiplying/Dividing Radical expressions

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  1. 7.1 and 7.2 Simplifying/Multiplying/Dividing Radical expressions

  2. Nth Roots

  3. For any real number a and b, and any positive integer n, if an = b , then a is the nth root of b.

  4. Real Number Examples: Find the roots: • Square Root of 4 Square Root of -4 • Cube Root of 8 Cube Root of -8 • Fourth Root of 16 Fourth Root of -16 • Fifth Root of 32 Fifth Root of -32

  5. Variable Examples: Find the Square Root of: • a1 2. a2 3. a3 4. a4

  6. When a number has two real roots, the positive root is called the principal root. • We always use the principal root when simplifying.

  7. Examples – Simplify : 1. 2.

  8. 3. 4.

  9. 5. 6.

  10. 7. 8. 9.

  11. 10. 11. 12.

  12. Multiplying and Dividing Radical Expressions • If they are real numbers, then

  13. Examples: 1. 2.

  14. 3. 4.

  15. 5. 6.

  16. Dividing Radical Expressions

  17. Examples: 1. 2.

  18. Rationalizing the Denominator **Multiply the numerator and denominator by the denominator** Then Simplify Example: 1.

  19. 2. 3.

  20. 4. 5.

  21. 7.3Adding, Subtracting, Multiplying and Dividing Binomial Radical Expressions

  22. Adding Radical Expressions • Use the same concept as that of adding or subtracting like variables. • Example: 7 - 3x + 2x + 5 *Have to have like Terms to Add/Subtract*

  23. Like Radicals are radical expressions that have the same index and the same radicand.

  24. Like Radicals Unlike Radicals = =

  25. Examples: 1. 2.

  26. 3. 4. 5. 6.

  27. Always simplify radicals before combining! 1. 2.

  28. 3. 4. 5. 6.

  29. Multiplying Radical Expressions When multiplying radicals, one must multiply the numbers OUTSIDE (O) the radicals AND then multiply the numbers INSIDE (I) the radicals.

  30. Dividing Radical Expressions When dividing radicals, one must divide the numbers OUTSIDE (O) the radicals AND then divide the numbers INSIDE (I) the radicals. Remember to rationalize the denominator if needed!

  31. Examples: 1. 2.

  32. Multiplying Binomials To multiply, USE FOIL! Example 1:

  33. 2. 3.

  34. Dividing Binomial Radicals To divide, Rationalize the denominator! (a + b)( a - b) = a2 – b2 These are called conjugates! They make radicals disappear!

  35. Examples: 1.

  36. 2.

  37. Solve: 1. 2.

  38. 3. 4.

  39. Examples: 1.

  40. 2.

  41. 3.

  42. 4.

  43. Homework Practice: Practice 7-3 #1-30 Left Column

  44. 7.4 Rational Exponents

  45. Homework Check

  46. Rational Exponents

  47. Rational Exponents are another way to write radicals.

  48. Simplify each expression. 1. 2.

  49. 3.

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