Simplifying Radicals Section 5.3

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 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, ….

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

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:

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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:

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

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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

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