SECONDARY MATH II // MODULE 3

SOLVING QUADRATICS & OTHER EQUATIONS – 3.2

Mathematics Vision Project

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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

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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