Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt1

Bruce Mayer, PE Chabot College Mathematics

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Chabot Mathematics

§7.3 Factor§7.3 FactorRadicalsRadicals



Review §Review §

Any QUESTIONS About• §7.3 → Multiply Radicals

Any QUESTIONS About HomeWork• §7.3 → HW-32

7.3 MTH 55



Product Rule for RadicalsProduct Rule for Radicals

For any real numbers and

That is, The product of two nth roots is the nth root of the product of the two radicands.



Simplifying by FactoringSimplifying by Factoring

The number p is a perfect square if there exists a rational number q for which q2 = p. We say that p is a perfect nth power if qn = p for some rational number q.

The product rule allows us to simplify whenever ab contains a factor that is a perfect nth power

n ab



Simplify by Product RuleSimplify by Product Rule

Use The Product Rule in REVERSE to Facilitate the Simplification process

• Note that and must both be real numbers

n n nab a b



Simplify a Radical Expression Simplify a Radical Expression with Index with Index nn by Factoring by Factoring

1. Express the radicand as a product in which one factor is the largest perfect nth power possible.

2. Take the nth root of each factor

3. Simplification is complete when no radicand has a factor that is a perfect nth power.



Example Example Simplify by Factoring Simplify by Factoring

Simplify by factoring (assume x > 0)a) b)

SOLUTION → Match INDICES a) b)





SOLN a)NoteThat theINDEXis 3





SOLN b) Note INDEX of 5




Simplify by factoring (assume x, y > 0)a) b)

SOLN a) Note INDEX of 2

4 15

2 15




Simplify by factoring (assume x, y > 0)a) b)

SOLN b) Note INDEX of 3

6 93 27 3 x x y

3 6 933 3 27 3x y x

2 33 3 3x y x



Example Example Simplify Simplify

Simplify by factoring (assume w, z > 0)

SOLN: First perform Distribution• Note that all INDICES are common at 5

5 965 75 64 428 zwwzzw

5 965 645 75 64

5 965 75 64

4828

428

zwzwwzzw

zwwzzw




SOLN: Use Radical Product Rule

SOLN: Use Commutative Property of Multiplication

5 96645 764

5 965 645 75 64

4828

4828

zwzwwzzw

zwzwwzzw

5 96645 764

5 96645 764

4828

4828

zzwwzzww

zwzwwzzw




SOLN: Exponent Product Rule

5 151055 1354

5 96645 7614

5 96645 764

22

3216

4828

zwzw

zwzw

zzwwzzww

SOLN: Next use Exponent POWER rule to expose as many bases as possible to the Power of 5; the Radical Index




SOLN: Power-to-Power Exponent Rule

5 535255 3525

5 151055 1354

216

22

zwzzw

zwzw

SOLN: Next Radical Product Rule

5 535 525 55 525 55 3

5 535255 3525

216

216

zwzwz

zwzzw




SOLN: Perform 5th Root Operations

SOLN: Finally Factor GCF = wz2

5 42323225 3

5 535 525 55 525 55 3

162216

216

zwzzwzwzwz

zwzwz

5 32

5 3232

162

162

zwzwz

zwzzw

ANS



WhiteBoard WorkWhiteBoard Work

Problems From §7.3 Exercise Set• 76, 80, 82, 92, 98

AdultCardiacIndex =2.8-3.4



All Done for TodayAll Done for Today

ExponentRules are

NOTAlgebraic



Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Chabot Mathematics

AppendiAppendixx

–

srsrsr 22



Graph Graph yy = | = |xx||

Make T-tablex y = |x |

-6 6-5 5-4 4-3 3-2 2-1 10 01 12 23 34 45 56 6

x

y

-6

-5

-4

-3

-2

-1

0

1

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-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

file =XY_Plot_0211.xls



-3

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0

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-3 -2 -1 0 1 2 3 4 5

M55_§JBerland_Graphs_0806.xls -5

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-10 -8 -6 -4 -2 0 2 4 6 8 10

M55_§JBerland_Graphs_0806.xls

x

y

Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

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