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Simplifying Radicals 3/21

Simplifying Radicals 3/21. 2 2 = 4 3 2 = 9 4 2 = 16 5 2 = 25 6 2 = 36 7 2 = 49 8 2 = 64 9 2 = 81 10 2 = 100 11 2 = 121 12 2 = 144. Simplifying Square Roots. These numbers in red are what we will be using to solve the questions.

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Simplifying Radicals 3/21

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  1. Simplifying Radicals 3/21 22= 4 32= 9 42= 16 52 = 25 62= 36 72= 49 82 = 64 92= 81 102= 100 112 = 121 122= 144 Simplifying Square Roots These numbers in red are what we will be using to solve the questions Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  2. Simplifying Radicals 3/21 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 125? Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  3. Simplifying Radicals 3/21 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 125? 125 / 25 = 5  * = Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  4. Simplifying Radicals 3/21 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 125? 125 / 25 = 5  * = Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  5. Simplifying Radicals 3/21 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 125? 25 * 5 = 125  * = 5 * = Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  6. Simplifying Radicals 3/21 Simplify Starting at the bottom of your list of perfect squares, which perfect square can divide evenly into 125? 25 * 5 = 125  * = 5 * = Final Answer: 5 Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  7. Simplify • 3 • 7 • 7 • 3 60 0 of 30

  8. Simplify • 4 • 5 • 10 • 2 60 0 of 30

  9. Student Practice • Please take out a sheet of paper, label it Classwork: Simplifying Radicals & Basic Trig • Complete the questions from the whiteboard • You have 10 minutes Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  10. Simplifying Radicals 3/21 You can only add or subtract if the radicand (number under the square root sign) is the same. Adding / Subtracting Radicals Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  11. Simplifying Radicals 3/21 Simplify the two expressions 2. Add or subtract the coefficients, leaving the radicand the same Adding / Subtracting Radicals Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  12. Simplifying Radicals 3/21 Simplify the two expressions 2. Add or subtract the coefficients, leaving the radicand the same Example: + =________ Adding / Subtracting Radicals Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  13. Simplifying Radicals 3/21 Simplify the two expressions 2. Add or subtract the coefficients, leaving the radicand the same Example: + =________ Adding / Subtracting Radicals Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  14. Simplifying Radicals 3/21 Simplify the two expressions 2. Add or subtract the coefficients, leaving the radicand the same Example: + =________ Final Adding / Subtracting Radicals Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  15. Simplifying Radicals 3/21 You can only add or subtract if the radicand (number under the square root sign) is the same. Example: Adding / Subtracting Radicals Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  16. Simplifying Radicals 3/21 Simplify the two expressions 2. Add or subtract the coefficients, leaving the radicand the same Example: These are different, can’t combine Adding / Subtracting Radicals Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  17. Simplifying Radicals 3/21 Simplify the two expressions 2. Add or subtract the coefficients, leaving the radicand the same Example: Final Answer Adding / Subtracting Radicals Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  18. Student Practice • Continue on your classwork page • Complete the questions from the whiteboard • You have 10 minutes Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  19. Simplifying Radicals 3/21 You can multiply radicals even if the radicand is different Multiplying Radicals Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  20. Simplifying Radicals 3/21 Multiplying radicals is a four step process: 1. Simplify both expressions. 2. Multiply both coefficients. 3. Multiply both radicands. 4. Check to see if the resulting radicand can be reduced further. Multiplying Radicals Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  21. Simplifying Radicals 3/21 1. Simplify both expressions. 2. Multiply both coefficients. 3. Multiply both radicands. 4. Check to see if the resulting radicand can be reduced further. Example: Multiplying Radicals Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  22. Simplifying Radicals 3/21 1. Simplify both expressions. 2. Multiply both coefficients. 3. Multiply both radicands. 4. Check to see if the resulting radicand can be reduced further. Example: Multiplying Radicals Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  23. Simplifying Radicals 3/21 1. Simplify both expressions. 2. Multiply both coefficients. 3. Multiply both radicands. 4. Check to see if the resulting radicand can be reduced further. Example: 2*3 = 6 Multiplying Radicals Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  24. Simplifying Radicals 3/21 1. Simplify both expressions. 2. Multiply both coefficients. 3. Multiply both radicands. 4. Check to see if the resulting radicand can be reduced further. Example: 2*3 = 6 Answer: 6 Multiplying Radicals Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  25. Simplifying Radicals 3/21 1. Simplify both expressions. 2. Multiply both coefficients. 3. Multiply both radicands. 4. Check to see if the resulting radicand can be reduced further. Example: 2*3 = 6 Final answer: 6 Multiplying Radicals Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  26. Student Practice • Continue on your classwork page • Complete the questions from the whiteboard • You have 10 minutes Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  27. Simplifying Radicals 3/21 If there are variables underneath the square root, divide the exponent by two. Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  28. Simplifying Radicals 3/21 If there are variables underneath the square root, divide the exponent by two. Example: Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  29. Simplifying Radicals 3/21 If there are variables underneath the square root, divide the exponent by two. Example: Divide the exponent by two, and drop the square root sign Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  30. Simplifying Radicals 3/21 If there are variables underneath the square root, divide the exponent by two. Example: x2 Divide the exponent by two, and drop the square root sign Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  31. Simplifying Radicals 3/21 If the exponent under the square root is odd: Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  32. Simplifying Radicals 3/21 If the exponent under the square root is odd: = * Separate it into two pieces Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  33. Simplifying Radicals 3/21 If the exponent under the square root is odd: = * x3 * Simplify the even exponent Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  34. Simplifying Radicals 3/21 If the exponent under the square root is odd: = * x3 * Final answer: x3 Simplifying Square Roots Mathematics.XEI.504.C: (24-27) manipulate radical expressions

  35. Simplify: • . x2 • . • 6x2 • 6 60 0 of 30

  36. Simplify: • x4y3 • x3y2 • x3y3 • x4y3 60 0 of 30

  37. Student Practice • Continue on your classwork page • Complete the questions from the whiteboard • You have 10 minutes Mathematics.XEI.504.C: (24-27) manipulate radical expressions

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