R7 - Section R.7 Radical Notation and Rational Exponents 2...

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Math 1513 Sec R.7 1 Section R.7 Radical Notation and Rational Exponents If 2 x a then x a or x a  . If n x a then x is said to be an nth root of a ( n x a ). Symbols like 3 6 , , are called radicals. Properties of Radicals 1. If n is even, | | n n a a . 2. If n is odd, n n a a . 3. n n n a b ab . 4. ( 0) n n n b a b a b . 5. ( ) m n n m a a . Rational Exponents Radical expressions can be rewritten using rational (fractional) exponents. For example, 1 2 5 5 and 5 1 5 3 3 . In general, for any real number a and any natural numbers m and n with 1 n 1. 1 n n a a . 2. ) ( m m n m n n a a a 3. 1 1 m n m m n n a a a
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Math 1513 Sec R.7 2 These properties, along with the properties of radicals and the properties of exponents we talked about earlier, allow us to work many types of problems involving radicals. Examples: a. Simplify: 3 x x 1 1 3 2 1 1 2 3 3 2 6 6 5 6 5 6 3 x x x x x x x x b.
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R7 - Section R.7 Radical Notation and Rational Exponents 2...

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