Download Square Roots and Pythagoras (Chapter 8)

Lesson1
*Calculatorsallowedforthisunit!
ExponentsandRoots
Exponentsarethesmallernumbersthatindicatehowmanytimesanumber(thebase)should
bemultipliedbyitself.
Baseà
174ßExponent
Whenwemultiplyanumberbyitself,wesquarethenumber.Weuseanexponentof2to
expressasquarednumber,e.g.,4×4=16=42.
Theproductsofsquarednumbersareperfectsquares,e.g.,16and225areperfectsquares.
Squaringandfindingasquarerootofanumberareinverse(opposite)operations.
42=16à√16=4
152=225à√225=15
Exponentsandrootscanalsogobeyondsquaresandsquareroots,e.g.,cubesandcuberoots.
43=64à∛64=4
133=2197à∛2197=13
Examples
Theareaofasquareis49cm2.Findthelengthofitssidestothenearestmm.
√49=7cm=70mm
Thevolumeofacubeis108m3.Findthelengthofitssidesto2decimalplaces.
∛108=4.76m
Which2consecutivewholenumbersis√17between?Basedonyourresponse,estimatethe
answerto1decimalplace.
√16=4
√25=5
Since17iscloseto16,√17isapproximatelyequalto4.2
Homework:p327,1,3,5;p3313-5,7-8
Lesson2
*Calculatorsallowedforthisunit!
Estimate:
o Theradiusofthesun,inkmà695,508km
o Theradiusoftheearth,inkmà6371km
o Thedistancefromearthtothesun,inkmà149600000km(1astronomicalunit)
o Thewidthofahumanhair,inmmà0.017–0.181mm
o Inkmà0.000000017-0.000000181km
Howcanwerepresentthesenumberssothattheycanbemoremeaningfullycompared?
ScientificNotation
Scientificnotationallowsmoremeaningfulcomparisonofnumbers,particularlyverylargeand
verysmallnumbers.
Scientificnotationismadeupoftwoparts:
1. Anumberthatis≥1and<10
2. Abase10exponent
e.g.,5.238×106.Itisdescribedas,“5.238times10tothepowerofsix”.
Theexponenttellsushowmanydecimalplacesthatweneedtomovetotheright(ifthe
exponentispositive)ortotheleft(iftheexponentisnegative)ifwewanttoexpandthe
numbertowriteitinstandardform.
e.g.,5.238×106[scientificnotation]=5,238,000[standardform]
Examples
Representtheanswerstothe4estimationproblemsusingscientificnotation.
695,508km=6.95508×105km
6371km=6.371×103km
149600000km=1.496×108km
0.000000017-0.000000181km=1.7×108km–1.81×107km
Writethefollowingnumbersinstandardform:
1.006×104
4.27×10-5
7.0054×10-2
Writethefollowingnumbersinscientificnotation:
780,120
127 0.0064
0.0008004
Whichnumberisgreater?9.7×105or3.01×106?Howdoyouknow?
Addthefollowingnumbers1.02×104,3.25×104,and6.8×104.
Is0.65×85writteninscientificnotation?Why/whynot?
Homework:p213-5,7-12,14;Handout(wordproblems)