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R8 Radicals and Rational Exponents Radical Notation n is called the index number a is called the radicand Properties of Radicals 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. • Simplifying Radicals 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 Simplify each radical expression Assume that all variables represent nonnegative real numbers. Assume that all variables represent nonnegative real numbers. Rewrite each of the following as a single number under the radical sign. 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 Assume that all variables represent nonnegative real numbers. Assume that all variables represent nonnegative real numbers. 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 Simplify each of the following radicals. Simplify each of the following radicals. Dividing Radicals 1.No radicals in the denominator 2.No fractions under the radicand 3.Apply the properties of radicals and exponents Assume that all variables represent nonnegative real numbers and that no denominators are zero. Assume that all variables represent nonnegative real numbers and that no denominators are zero. Assume that all variables represent nonnegative real numbers and that no denominators are zero. Assume that all variables represent nonnegative real numbers and that no denominators are zero. Simplify each of the following radicals. Rational Exponents Rational Exponents Simplify each expression containing fractional exponents as radicals. Simplify each expression using radicals and exponents. Simplify each expression using radicals or exponents. Simplifying each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. Simplifying each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. Simplifying each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive.