6.2RadicalsandRationalExponentsDefinitions:

RadicalIndexnthroot

Letslookatsomeexamples!Example1:FindingnthrootsFindtheindicatedrealnthroot(s)ofa.

a) ! = 3,! = −27

b) ! = 4,! = 16

c) ! = 3,! = −125

d) ! = 4,! = −81

RationalExponents(Fractionsasexponents)

a) (16)!!

b) (−27)!!

c) (5)!!

d) (!)!!

Example2:Evaluatingnthrootexpressions

Example4:SolvingaReal-LifeProblemTheformulatofindthevolumeofasphereis! = !

!!!!.

a) Solvetheequationforr

b) Findtheradiusofthebeachball

Example5:SolvingReal-LifeProblemTocalculatetheannualinflationrater(indecimalform)ofanitemthatincreasesinvaluefromPtoF

overaperiodofnyears,youcanusetheequation! = !!

!! − 1

Findtheannualinflationratetothenearesttenthofapercentofahousethatincreasesinvaluefrom$200,000to$235,000overaperiodof5years.Homework3-6,8,10,12,14-18even,19-22,24,26,28,31,32,37,41