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Simplifying Radicals

Topic: Radical Expressions Essential Question: How are radical expressions represented and how can you solve them?. Simplifying Radicals. What numbers are perfect squares?. 1 • 1 = 1 2 • 2 = 4 3 • 3 = 9 4 • 4 = 16 5 • 5 = 25 6 • 6 = 36

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Simplifying Radicals

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  1. Topic: Radical Expressions Essential Question: How are radical expressions represented and how can you solve them? Simplifying Radicals

  2. What numbers are perfect squares? 1 • 1 = 1 2 • 2 = 4 3 • 3 = 9 4 • 4 = 16 5 • 5 = 25 6 • 6 = 36 49, 64, 81, 100, 121, 144, ...

  3. A List of Some Perfect Squares 64 225 1 81 256 4 100 289 9 121 16 324 144 25 400 169 36 196 49 625

  4. Simplify = 2 = 4 That was easy! = 5 = 10 = 12

  5. Perfect Square Factor * Other Factor Simplify = = = = LEAVE IN RADICAL FORM = = = = = =

  6. Perfect Square Factor * Other Factor Simplify = = = = LEAVE IN RADICAL FORM = = = = = =

  7. 1. Simplify

  8. Simplify • . • . • . • .

  9. Combining Radicals + To combine radicals: combine the coefficients of like radicals Hint: In order to combine radicals they must be like terms

  10. Simplify each expression

  11. Simplify each expression: Simplify each radical first and then combine.

  12. Simplify each expression: Simplify each radical first and then combine.

  13. Simplify each expression

  14. Simplify each expression

  15. Multiplying Radicals * To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals. Hint: to multiply radicals they DO NOT need to be like terms

  16. Multiply and then simplify

  17. Dividing Radicals To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator

  18. That was easy!

  19. Simplify Uh oh… There is a radical in the denominator! Whew! It simplified!

  20. Uh oh… Another radical in the denominator! Simplify Whew! It simplified again! I hope they all are like this!

  21. This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator. 42 cannot be simplified, so we are finished.

  22. Uh oh… There is a fraction in the radical! Simplify Since the fraction doesn’t reduce, split the radical up. How do I get rid of the radical in the denominator? Multiply by the “fancy one” to make the denominator a perfect square!

  23. This can be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

  24. This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator. Reduce the fraction.

  25. Simplify = X = Y3 = P2X3Y = 2X2Y = 5C4D5

  26. Simplify = = = =

  27. Simplify • . • . • . • .

  28. Challenge: Since there are no like terms, you can not combine.

  29. How do you know when a radical problem is done? • No radicals can be simplified.Example: • There are no fractions in the radical.Example: • There are no radicals in the denominator.Example:

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