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Simplifying Radicals

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

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**How do you simplify variables in the radical?**

Look at these examples and try to find the pattern… What is the answer to ? As a general rule, divide the exponent by two. The remainder stays in the radical.

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**Simplifying variable radicands**

X² X

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Simplify = = = This is a piece of cake! = =

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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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**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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**+ To combine radicals: combine the coefficients of like radicals**

Combining Radicals + To combine radicals: combine the coefficients of like radicals

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**Simplify each expression**

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**Simplify each expression**

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**Simplify each expression: Simplify each radical first and then combine.**

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**Simplify each expression: Simplify each radical first and then combine.**

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**Simplify = = = = = = = = = = Perfect Square Factor * Other Factor**

LEAVE IN RADICAL FORM = = = = = =

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**Simplify each expression**

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**Simplify each expression**

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WORKSHEET 3)

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5) 7)

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9)

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11)

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13)

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15)

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17)

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Multiplying Radicals * To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.

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**Multiply and then simplify**

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WORKSHEET(MULT)

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WORKSHEET(MULT)

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WORKSHEET(MULT)

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WORKSHEET(MULT)

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WORKSHEET(MULT)

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WORKSHEET(MULT)

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**Using distributive Property**

a(b+c) = ab + ac a(b-c) = ab - ac

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**USING THE DISTRIBUTIVE PROPERTY**

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**USING THE DISTRIBUTIVE PROPERTY**

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**USING THE DISTRIBUTIVE PROPERTY**

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**USING THE DISTRIBUTIVE PROPERTY**

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**USING THE DISTRIBUTIVE PROPERTY**

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**USING THE DISTRIBUTIVE PROPERTY**

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**USING THE DISTRIBUTIVE PROPERTY**

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**USING THE DISTRIBUTIVE PROPERTY**

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Using the FOIL

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Using the FOIL

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Using the FOIL

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Dividing Radicals To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator

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That was easy!

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**42 cannot be simplified, so we are finished.**

This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator. 42 cannot be simplified, so we are finished.

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**This can be divided which leaves the radical in the denominator**

This can be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

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**This cannot be divided which leaves the radical in the denominator**

This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

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**This cannot be divided which leaves the radical in the denominator**

This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

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**How do you simplify variables in the radical?**

Look at these examples and try to find the pattern… What is the answer to ? As a general rule, divide the exponent by two. The remainder stays in the radical.

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**How do you simplify variables in the radical?**

Look at these examples and try to find the pattern… As a general rule, divide the exponent by two.

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Simplify = = = = =

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Simplify = = = = =

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Simplify = = = =

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= = ? = =

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