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Geometry Day 54

Geometry Day 54. Radicals. Today’s Agenda. Radicals Definition Simplifying Adding/Subtracting Multiplying Dividing Rationalizing the denominator. Radicals - definitions. The definition of is the number that when multiplied by itself 2 times is x. Simplifying radicals.

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Geometry Day 54

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  1. Geometry Day 54 Radicals

  2. Today’s Agenda • Radicals • Definition • Simplifying • Adding/Subtracting • Multiplying • Dividing • Rationalizing the denominator

  3. Radicals - definitions The definition of is the number that when multiplied by itself 2 times is x.

  4. Simplifying radicals Most numbers are not perfect squares, but may have a factor(s) that is (are) a perfect square(s). The perfect squares are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, …. Rewrite these numbers by factoring out as many perfect squares as possible: 200 18 45 242 32 38 400 27 75 72

  5. Try these - simplify: If a radical has a perfect square factor, then we can pull it out from under the sign. Ex:

  6. Adding or Subtracting Radicals To add or subtract square roots you must have like radicands (the number under the radical). Sometimes you must simplify first:

  7. Try These

  8. Multiplying Radicals You can multiply any square roots together. Multiply any whole numbers together and then multiply the numbers under the radical and reduce. Try these:

  9. Dividing Radicals To divide square roots, divide any whole numbers and then divide the radicals one of two ways: 1) divide the numbers under the radical sign and then take the root, OR 2) take the root and then divide. Be sure to simplify. or

  10. Try These

  11. Rationalizing Radicals • It is good practice to eliminate radicals from the denominator of an expression. • For example: • We do not want to change the value of the expression, so we need to multiply the fraction by 1. But “1” can be written in many ways… We need to eliminate Since we will multiply by one where

  12. Try These

  13. Homework 30 • Packet, Radical Operations

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