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Simplifying Square Roots and Factor Trees Explained

Learn how to simplify square roots and make factor trees to find prime factors. Understand the basics of radical expressions and perfect squares. Complete homework assignments by following step-by-step methods.

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Simplifying Square Roots and Factor Trees Explained

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  1. Warm Up 09-08-09 Make a factor tree showing the prime factors for the following numbers: 48 63 80 92 128

  2. Radical Expressions Simplifying Square Roots

  3. Square roots radical expression • Square roots are one type of _______ __________. • When asking for the “square root” of 36 you are asking for a number that, when ________ by ______ equals ____. multiplied itself 36 = 6 radical sign radicand

  4. To Simplify Radical Expressions We just work with this today All of the following must be true… • The radical has no perfect square factors other than 1. (Twins make a perfect square) • The radicand has no fractions. • There are no square roots in any denominator.

  5. Simplify the Square Roots = 7 • What about ? • 50 is not a _______ _______. perfect square • so we will simplify… 2 methods You choose which you prefer.

  6. Simplify Square Roots – Method 1 • Factor out the perfect square roots Check with a calculator to see that these match

  7. Simplify Square Roots – Method 2-Helpful when you don’t know perfect squares! • Factor the number in the radicand down to prime numbers and simplify. (Look for twins…they make perfect squares) 2 50 25 5 5

  8. Simplify • Method 1… • Method 2… 2 54 27 3 9 3 3

  9. Simplify • Method 1… • Method 2… 48 2 24 2 12 2 6 2 3

  10. What about… No Perfect Square Factors No twins! Leave it as it is

  11. Your turn! Simplify Using Either Method

  12. HOMEWORK Write these out on your own paper before you leave class. Simplify the radicals…..Show your work!!!

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