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Simplifying Radicals

Simplifying Radicals. Perfect Squares. 64. 225. 1. 81. 256. 4. 100. 289. 9. 121. 16. 324. 144. 25. 400. 169. 36. 196. 49. 625. Simplify. = 2. = 4. = 5. This is a piece of cake!. = 10. = 12. Steps for Simplifying Radicals

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Simplifying Radicals

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  1. Simplifying Radicals

  2. Perfect Squares 64 225 1 81 256 4 100 289 9 121 16 324 144 25 400 169 36 196 49 625

  3. Simplify = 2 = 4 = 5 This is a piece of cake! = 10 = 12

  4. Steps for Simplifying Radicals • Write the prime factorization of your radicand. • 2. Determine the index of the radical. • 3. If the index is 2, circle groups of 2 identical numbers or variables. If the index is 3, circle groups of 3 identical numbers or variables, etc. • 4. The number or variable from each circled group will show up outside the radical symbol 1 time. • 5. Anything left uncircled will remain under the radical. If everything under the radical symbol is circled, the radical symbol will disappear. • 6. Multiply the numbers and variables outside the radical together.

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

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

  7. Combining Radicals + To combine radicals: combine the coefficients of like radicals

  8. Simplify each expression

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

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

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

  12. Simplify each expression

  13. Simplify each expression

  14. Multiplying Radicals * To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.

  15. Multiply and then simplify

  16. 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

  17. That was easy!

  18. 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.

  19. 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.

  20. 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.

  21. Simplify = X = Y3 = P2X3Y = 2X2Y = 5C4D10

  22. Simplify = = = =

  23. = = ? = =

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