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SECONDARY MATH II // MODULE 3
SOLVING QUADRATICS & OTHER EQUATIONS – 3.2
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
3.2
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READY Topic:SimplifyingRadicalsAverycommonradicalexpressionisasquareroot.Onewaytothinkofasquarerootisthenumberthatwillmultiplyby itself tocreateadesiredvalue.Forexample: 2is thenumber thatwillmultiplyby itself toequal2.And in likemanner 16isthenumberthatwillmultiplybyitselftoequal16,inthiscasethevalueis4because4x4=16.(Whenthesquarerootofasquarenumber istakenyougetanicewholenumbervalue.Otherwiseanirrationalnumber isproduced.)Thissamepatternholdstrueforotherradicalssuchascuberootsandfourthrootsandsoforth.Forexample: 8! isthenumberthatwillmultiplybyitselfthreetimestoequal8.Inthiscaseitisequaltothevalueof2because2!=2x2x2=8.Withthisinmindradicalscanbesimplified.Seetheexamplesbelow.
Example1:Simplify 2020= 4 ∙ 5 = 2 ∙ 2 ∙ 5=2 5
Example2:Simplify 96! 96! = 2! ∙ 3! =2 3!
Simplifyeachoftheradicals.1. 40 2. 50 3. 16!
4. 72 5. 81! 6. 32
7. 160! 8. 45 9. 54!
READY, SET, GO! Name PeriodDate
SECONDARY MATH II // MODULE 3
SOLVING QUADRATICS & OTHER EQUATIONS – 3.2
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
3.2
Needhelp?Visitwww.rsgsupport.org
SET Topic:FindingarithmeticandgeometricmeansandmakingmeaningofrationalexponentsYoumayhavefoundarithmeticandgeometricmeansinyourpriorwork.Findingarithmeticandgeometricmeansrequiresfindingvaluesofasequencebetweengivenvaluesfromnon-consecutiveterms.Ineachofthesequencesbelowdeterminethemeansandshowhowyoufoundthem.Findthearithmeticmeansforthefollowing.Showyourwork.10.
x 1 2 3y 5 11
11.
x 1 2 3 4 5y 18 a. b. c. -10
12.
x 1 2 3 4 5 6 7y 12 a. b. c. d. e. -6
Findthegeometricmeansforthefollowing.Showyourwork.13.14.15.Fillinthetablesofvaluesandfindthefactorusedtomovebetweenwholenumbervalues,Fw,aswellasthefactor,Fc,usedtomovebetweeneachcolumnofthetable.16.
d.Fw=e.Fc=
x 1 2 3y 3 12
x 1 2 3 4y 7 a. b. 875
x 1 2 3 4 5 6y 4 a. b. c. d. 972
x 0
€
12 1
€
32 2
y 4 a. 16 b. c.
Fw
Fw
SECONDARY MATH II // MODULE 3
SOLVING QUADRATICS & OTHER EQUATIONS – 3.2
Mathematics Vision Project
Licensed under the Creative Commons Attribution CC BY 4.0
mathematicsvisionproject.org
3.2
Needhelp?Visitwww.rsgsupport.org
17.d.Fw=e.Fc=
18.
d.Fw=e.Fc=
GO Topic:SimplifyingExponents
Findthedesiredvaluesforeachfunctionbelow.
19.𝑓(𝑥) = 2𝑥 − 7
20.𝑔 𝑥 = 3! 2 21.𝐼(𝑡) = 210 1.08!
a. Find𝑓(−3)
b. Find𝑓(𝑥) = 21
c. Find𝑓 !!
a. Find𝑔(−4)
b. Find𝑔(𝑥) = 162
c. Find𝑔 !!
a. Find𝐼(12)
b. Find𝐼(𝑡) = 420
c. Find𝐼 !!
22.ℎ(𝑥) = 𝑥! + 𝑥 − 6
23.𝑘(𝑥) = −5𝑥 + 9
24.𝑚(𝑥) = (5!)2
a. Findℎ(−5)
b. Findℎ(𝑥) = 0
c. Findℎ !!
a. Find𝑘(−7)
b. Find𝑘(𝑥) = 0
c. Find𝑘 !!
a. Find𝑚(−2)
b. Find𝑚(𝑥) = 1
c. Find𝑚 !!
x 0
€
12 1
€
32 2
y 4 a. 8 b. c.
x 0
€
12 1
€
32 2
y 5 a. 15 b. c.
Fw
Fw
Fw
Fw
