Simplifying Radicals Section 5 3 n Radicals n

Simplifying Radicals Section 5. 3

n Radicals n Definition n Simplifying n Adding/Subtracting n Multiplying n Dividing n 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 n It is good practice to eliminate radicals from the denominator of an expression. n For example: We need to eliminate n 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… Since we will multiply by one where

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