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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**Simplify**= 2 = 4 = 5 This is a piece of cake! = 10 = 12**Perfect Square Factor * Other Factor**Simplify = = = = LEAVE IN RADICAL FORM = = = = = =**Perfect Square Factor * Other Factor**Simplify = = = = LEAVE IN RADICAL FORM = = = = = =**Combining Radicals**+ To combine radicals: combine the coefficients of like radicals**Simplify each expression: Simplify each radical first and**then combine.**Simplify each expression: Simplify each radical first and**then combine.**Perfect Square Factor * Other Factor**Simplify = = = = LEAVE IN RADICAL FORM = = = = = =**Multiplying Radicals*** To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.**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**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.**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.**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. Reduce the fraction.**Simplify**= X = Y3 = P2X3Y = 2X2Y = 5C4D10**Simplify**= = = =**=**= ? = =