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
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