Roots-and-Radical-Expressions7根和根的表达式课件

1、7. Roots and Radical ExpressionsIn this chapter, you will learn:What a polynomial isAdd/subtract/multiply/divide polynomialsSimplify radicals, exponentsSolving equations with exponents and radicalsComplex numbersConjugatesWhat is a monomial?An expression that is a number, that may or may not include

2、 a variable.MONOMIALSNOT MONOMIALSReal RootsReal roots are the possible solutions to a number, raised to a power. Vocabulary and PropertiesindexRadical signradicandHow to find the root (other than a square root), using a graphing calculator 1. Input the root you are going to take (for example, if yo

3、u are taking the third root of a number, start with the 3).2.Press MATH and select option 53. Enter the value you are taking the root of.Ex: 4 MATH 5 81 ENTER3Practice: Find each rootSolutions: 22, 7, and ERR: NONREAL ANS Lets take a closer look at this answerProperties and Notation:When n is an eve

4、n numberWhy? We want to make sure that the root is always positive when the index is an even numberNote: Absolute value symbols ensure that the root is positive when x is negative. They are not needed for y because y2 is never negative. Absolute value symbols must not be used here. If x is negative,

5、 then the radicand is negative and the root must also be negative. Notice that the index is an odd number here . . .Lets try someSimplify each expression. Use the absolute value symbols when needed. SolutionsSimplify each expression. Use the absolute value symbols when needed. Properties of Exponents lets review . . . NEGATIVE EXPONENTRULEPRODUCT OR POWERRULEHAVE TO HAVE THESAME BASEQUOTIENT OF POWERRULEHAVE TO HAVE THESAME BASEPOWER OF POWERRULE(x4)POWER OF PRODUCTRULE(2x4)POWER OF A QUOTIENTRULEPOWER OF QUOTIENT 2RULEFracti