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R8 Radicals and Rational Exponent s

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Radical Notation n is called the index number a is called the radicand

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Properties of Radicals

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Simplifying Radicals 1.The radicand has no factor raised to a power greater than or equal to the index number. 2.The radicand has no fractions. 3.No denominator contains a radical. 4.Exponents in the radicand and the index of the radical have no common factor. 5.All indicated operations have been performed

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If there is no index #, it is understood to be 2 When simplifying radicals use perfect squares, cubes, etc. Use factor trees to break a number into its prime factors Apply the properties of radicals and exponents Simplifying Radicals

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Simplify each radical expression

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Assume that all variables represent nonnegative real numbers.

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Rewrite each of the following as a single number under the radical sign.

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Multiplying Radicals 1.Radicals must have the same index number 2. Multiply outsides and insides together 3. Add exponents when multiplying 4. Simplify your expression 5. Combine all like terms

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Assume that all variables represent nonnegative real numbers.

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Add/Subtract Radicals 1.Simplify each radical expression 2.Radicals must have the same index number and same radicand 3.Add the outside numbers together and the radicand remains the same

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Simplify each of the following radicals.

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Dividing Radicals 1.No radicals in the denominator 2.No fractions under the radicand 3.Apply the properties of radicals and exponents

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Assume that all variables represent nonnegative real numbers and that no denominators are zero.

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Simplify each of the following radicals.

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Rational Exponents

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Simplify each expression containing fractional exponents as radicals.

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Simplify each expression using radicals and exponents.

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Simplify each expression using radicals or exponents.

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Simplifying each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive.

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