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**Radicals are in simplest form when:**

No factor of the radicand is a perfect square other than 1. The radicand contains no fractions No radical appears in the denominator of a fraction

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Perfect Squares 64 225 1 81 256 4 100 289 9 121 16 324 144 25 400 169 36 49 196 625

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**Multiplication property of square roots:**

Division property of square roots:

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Simplify = 2 = 4 = 5 This is a piece of cake! = 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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**Simplify = = = = = = = = Perfect Square Factor * Other Factor**

LEAVE IN RADICAL FORM = = = =

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**Simplify = = = = = = = = = = 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: 20 10 2 5

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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. The radicand contains no fractions No radical appears in the denominator of a fraction

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**REMEMBER THE PRODUCT PROPERTY OF SQUARE ROOTS:**

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

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**4 Multiply Square Roots To multiply square roots –**

you multiply the radicands together then simplify EX: * = = 4 Simplify =

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Try These : * * *

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Let’s 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 1. 2. 3. 4. 5.

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**Radicals are in simplest form when:**

No factor of the radicand is a perfect square other than 1. The radicand contains no fractions No 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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**Hint – you will need to rationalize the denominator**

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

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**Review writing in simplest radical form:**

1) 2) 3) 4) 5) 6)

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**Review writing in simplest radical form:**

7) 8) 9)

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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 same

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