1、7.Roots and Radical ExpressionsIn this chapter,you will learn:What a polynomial is Add/subtract/multiply/divide polynomials Simplify radicals,exponents Solving equations with exponents and radicals Complex numbers ConjugatesWhat is a monomial?An expression that is a number,that may or may not includ
2、e a variable.x42x2xy10MONOMIALSNOT MONOMIALSx48x x518Real Roots Real roots are the possible solutions to a number,raised to a power.powerfourth the to16 of roots are 2 negative and 2both so16)2(2445?)beit t can(why 125-ofroot real possibleonly theis 5-so12553power second the x toof rootsarex-andboth
3、 x so2xxorxxxVocabulary and PropertiesnaindexRadical 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 you are taking the third root of a number,start with the 3).2.Press MATH and select option 53.Enter the va
4、lue you are taking the root of.Ex:x4814 MATH 5 81 ENTER3Practice:Find each root310648516807Solutions:22,7,and ERR:NONREAL ANS 416Lets take a closer look at this answerProperties and Notation:aanWhen n is an even numberWhy?We want to make sure that the root is always positive when the index is an eve
5、n numberpositive.staysit sure make to valueabsolute theuse Weforwards.andbackwards trueisit that so indexeseven with positive a always is that x sure make want to we525)5(,5 if BUT5255,5 IF:itat look y toanother wa sHere2222soxxxxxx2442444842)()2(16:yxyxyxexNote:Absolute value symbols ensure that th
6、e root is positive when x is negative.They are not needed for y because y2 is never negative.23323363)(:yxyxyxexAbsolute value symbols must not be used here.If x is negative,then the radicand is negative and the root must also be negative.Notice that the index is an odd number here.Lets try some3627
7、yxSimplify each expression.Use the absolute value symbols when needed.424yxSolutions3627yxSimplify each expression.Use the absolute value symbols when needed.424yxProperties of Exponents lets review.NEGATIVE EXPONENTRULEnna1a25251PRODUCT OR POWERRULE201022nmnmaaa302HAVE TO HAVE THESAME BASEQUOTIENT
8、OF POWERRULE4103363babaxxxHAVE TO HAVE THESAME BASEPOWER OF POWERRULE(x4)34x12xmnnma)a(POWER OF PRODUCTRULEmnnnmba)ab(2x4)545x220 x32POWER OF A QUOTIENTRULEababnnnFHGIKJ35yFHGIKJ355yPOWER OF QUOTIENT 2RULE2y322y3223y92yaaaxyyxFractional Exponents(Powers and Roots)xyyxyxaaa)(“Power”“Root”RADICAL TO EXPONENTRULE251 2/aa1 2/25 5aann1/RATIONAL EXPONENTRULEmnnmnmaaa43163416 328
