tailieunhanh - Mathematics - Lecture 5: Radical expressions and rational exponents

Mathematics - Lecture 5 "Radical expressions and rational exponents" presents the following content: nth root of anpha, simplification of radical expressions, operations involving radical expressions, rationalizing radical expressions. | Radical Expressions and Rational Exponents Mathematics 17 Institute of Mathematics, University of the Philippines-Diliman Lecture 5 Math 17 (UP-IMath) Radical Expressions and Rational Exponents Lec 5 1 / 23 Outline 1 Radical Expressions nth root of a Simplification of Radical Expressions Operations Involving Radical Expressions Addition and Subtraction of Radical Expressions Multiplication and Division of Radical Expressions Rationalizing Radical Expressions Math 17 (UP-IMath) Radical Expressions and Rational Exponents Lec 5 2 / 23 nth root of a Definition Let a, b ∈ R and n ∈ N, n > 1. If bn = a then b is an nth root of a. Math 17 (UP-IMath) Radical Expressions and Rational Exponents Lec 5 3 / 23 nth root of a Definition Let a, b ∈ R and n ∈ N, n > 1. If bn = a then b is an nth root of a. Examples: Since both 32 , (−3)2 are equal to 9, then 3 and -3 are second roots or square roots of 9. -4 is a third root or a cube root of -64 since (−4)3 = −64. 2 and -2 are fourth roots of 16 since (−2)4 = (2)4 = 16. Math 17 (UP-IMath) Radical Expressions and Rational Exponents Lec 5 3 / 23 Principal nth root of a Definition √ If n ∈ N, n > 1, a ∈ R, the principal nth root of a, denoted n a, is defined as follows: √ If a > 0, then n a is the nth root of a that is positive. √ If a < 0 and n is odd, then n a is the nth root of a that is negative. √ If a is zero, then n 0 = 0. Math 17 (UP-IMath) Radical Expressions and Rational Exponents Lec 5 4 / .