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Chapter 10 Exponents & Radicals Phong Chau

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Section 10.1 Radical Expressions & Functions

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Definition Q: What number when squared equals 36? A: 6 Q: Is it the only answer? A: No 6 is called a square root of 36 -6 is also a square root of 36 Def: b is called a square root of the number a if b 2 =a.

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Examples A square root of 36 is 6 Another square root of 36 is -6 A square root of 121 is 11 Another square root of 121 is -11 A square root of 0 is 0 A square root of -4 is Remarks: 1)Each positive number has two square roots: a positive square root and a negative square root 2)0 has a unique square root 3)Each negative number has no square root. NONE

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Notation The positive square root of a number a is denoted by the radical symbol: It’s also called the principal square root of a. Examples:

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Definition Def: b is called an n th root of the number a if b n =a. The principal n th root of a is denoted by index of the radical radical symbol radicand Q: What number when cubed equals 8? A: 2 Q: What number when raised to the fifth power equals -32? A: -2 because

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Examples No such real number exists

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Examples Evaluate the following radical expressions

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Examples Evaluate the following radical expressions When the index is odd When the index is even

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Examples Simplify the expressions When n is odd When n is even

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Radical Functions Graph the following functions Find the domain of the following functions

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