9.1PropertiesofRadicalsWhataresomerulesyoucanrecallaboutradicals?Simplestform:

• Noradicandshaveaperfectnthpowerasfactorsotherthan1• Noradicandscontainfractions• Noradicandsappearinthedenominatorofafraction

Example1:UsingtheProductPropertyofSquareRootsSimplifythefollowing

a) 5 ∙ 5 b. 3 ∙ 12 c. 108 d. 9)*Example2:UsingtheQuotientPropertyofSquareRootsSimplifythefollowing

a) +,- b. ,.

/0 c. /,01 d. 2/

34

Example3:UsingPropertiesofCubeRootsSimplifythefollowing

a) 647 b. 125)*7 c. −27);7 d. <+/0

7

Tryonyourown:RationalizingtheDenominator:

a) /, +

,0 = b) 3*

Example4:RationalizingtheDenominator

a) ,*? b)

+-7

Example5:RationalizingtheDenominatorUsingConjugatesSimplifythefollowing:

72 − 3

Tryonyourown:

Example6:SolvingaRealLifeProblemThedistanced(inmiles)thatyoucanseetothehorizonwithyoureyelevelhfeetabovethewaterisgivenby

@ = *A+ .Howfarcanyouseewhenyoureyelevelis5ftabovethewater?Findtheexactandestimated

distance.Example7:ModelingwithMathematicsTheratioofthelengthtothewidthofagoldenrectangleis 1 + 5 ∶ 2.ThedimensionsofthefaceoftheParthenoninGreeceformagoldenrectangle.WhatistheheighthoftheParthenon?Example8:AddingandSubtractingRadicalsSimplifythefollowing:(Thinkliketerms)

A) 5 7 + 11 − 8 7 b)10 5 + 20 c)6 )7 + 2 )7 Homework:5-59odd