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Radicals are in simplest form when: No factor of the radicand is a perfect square other than 1.No factor of the radicand is a perfect square other than 1. The radicand contains no fractionsThe radicand contains no fractions No radical appears in the denominator of a fractionNo radical appears in the denominator of a fraction

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Perfect Squares

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Multiplication property of square roots: Division property of square roots:

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= 2 = 4 = 5 = 10 = 12

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To Simplify Radicals you must make sure that you do not leave any perfect square factors under the radical sign. *Think of the factors of the radicand that are perfect squares. Perfect Square Factor * Other Factor = = LEAVE IN RADICAL FORM

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= = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM

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= = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM

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If you cannot think of any factors that are perfect squares – prime factor the radicand to see if you have any repeated factors EX:

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You can simplify radicals that have variables TOO! = = = = =

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Radicals are in simplest form when: No factor of the radicand is a perfect square other than 1.No factor of the radicand is a perfect square other than 1. The radicand contains no fractionsThe radicand contains no fractions No radical appears in the denominator of a fractionNo radical appears in the denominator of a fraction

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Multiply Square Roots REMEMBER THE PRODUCT PROPERTY OF SQUARE ROOTS: OR

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Multiply Square Roots To multiply square roots – you multiply the radicands together then simplify EX: *== Simplify= 4

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Try These : * * *

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Lets try some more:

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Multiply Square Roots Multiply the coefficients Multiply the radicands Simplify the radical.

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Multiply & Simplify Practice

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Homework Practice

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Radicals are in simplest form when: No factor of the radicand is a perfect square other than 1.No factor of the radicand is a perfect square other than 1. The radicand contains no fractionsThe radicand contains no fractions No radical appears in the denominator of a fractionNo radical appears in the denominator of a fraction

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Division property of square roots:

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To simplify a radicand that contains a fraction – first put a separate radical in the numerator and denominator Then simplify

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Try These : Simplify:

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If we have a radical left in the denominator then we must rationalize the denominator: == Since we cannot leave a radical in the denominator we must multiply both the numerator and the denominator by this radical to rationalize * = =

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Simplify: Hint – you will need to rationalize the denominator A. B. 4 C. D. 16

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Simplify Radicals 1)2)3)4)

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5) 6) 7) 8) Simplify some more:

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Review writing in simplest radical form: 1) 2) 3) 4) 5) 6)

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7) 8) 9) Review writing in simplest radical form:

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Which of the following is not a condition of a radical expression in simplest form? A. No radicals appear in the numerator of a fraction. B. No radicands have perfect square factors other than 1. C. No radicals appear in the denominator of a fraction. D. No radicands contain fractions.

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Adding and subtracting radical expressions You can only add or subtract radicals together if they are like radicals – the radicands MUST be the sameYou can only add or subtract radicals together if they are like radicals – the radicands MUST be the same

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