Dividing and Simplifying Radicals

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Dividing and SimplifyingRadicals

• Geometry
• Lesson
• Radicals Section C

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Dividing with Radicals

• Compare the following square roots.
• What do you notice about the results?

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Division Property for Radicals

• From the last slide a relationship suggests the
  following fact about square roots.
• For any nonnegative real numbers a and b, where b
  ? 0,
• and
  

4
Fractional Radicands

• Fractional radicands with a perfect square
  numerator and a perfect square denominator can be
  simplified.
• Examples Simplify.
• 1.
• 2.

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More Fractional Radicands

• Sometimes a fractional radicand can be simplified
  to a perfect square.
• 3.
• 4.

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Using the Division Property

• We can use the division property for radicals to
  simplify radicals with fractions and to divide
  radicals.
• 5.
• 6.

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Rationalizing the Denominator

• An expression containing radicals is simplified
  when the following conditions are met.
• The radicand contains no perfect square factors.
• A fraction in simplest form does not have a
  radical in the denominator.
• A simplified radical does not contain a
  fractional radicand.

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More from Last Slide

• The process of removing a fraction from the
  radicand or a radical from the denominator is
  called rationalizing the denominator.
• 7.
• 8.

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More Examples

• 9.
• 10.

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More Rationalizing the Denominator

• If the radicand is a fraction, it can be
  simplified by writing it as a division of
  radicals and proceeding as before.
• 11.
• 12.

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More Examples

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Assignment

• W.S. 11-5
• 3 63 by 3s