[email protected] mth55_lec-42_sec_7-3b_factor_radicals.ppt 1 bruce mayer, pe chabot college...
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[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt1
Bruce Mayer, PE Chabot College Mathematics
Bruce Mayer, PELicensed Electrical & Mechanical Engineer
Chabot Mathematics
§7.3 Factor§7.3 FactorRadicalsRadicals
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt2
Bruce Mayer, PE Chabot College Mathematics
Review §Review §
Any QUESTIONS About• §7.3 → Multiply Radicals
Any QUESTIONS About HomeWork• §7.3 → HW-32
7.3 MTH 55
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt3
Bruce Mayer, PE Chabot College Mathematics
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.
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt4
Bruce Mayer, PE Chabot College Mathematics
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
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt5
Bruce Mayer, PE Chabot College Mathematics
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
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt6
Bruce Mayer, PE Chabot College Mathematics
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.
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt7
Bruce Mayer, PE Chabot College Mathematics
Example Example Simplify by Factoring Simplify by Factoring
Simplify by factoring (assume x > 0)a) b)
SOLUTION → Match INDICES a) b)
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt8
Bruce Mayer, PE Chabot College Mathematics
Example Example Simplify by Factoring Simplify by Factoring
Simplify by factoring (assume x > 0)a) b)
SOLN a)NoteThat theINDEXis 3
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt9
Bruce Mayer, PE Chabot College Mathematics
Example Example Simplify by Factoring Simplify by Factoring
Simplify by factoring (assume x > 0)a) b)
SOLN b) Note INDEX of 5
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt10
Bruce Mayer, PE Chabot College Mathematics
Example Example Simplify by Factoring Simplify by Factoring
Simplify by factoring (assume x, y > 0)a) b)
SOLN a) Note INDEX of 2
4 15
2 15
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt11
Bruce Mayer, PE Chabot College Mathematics
Example Example Simplify by Factoring Simplify by Factoring
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
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt12
Bruce Mayer, PE Chabot College Mathematics
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
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt13
Bruce Mayer, PE Chabot College Mathematics
Example Example Simplify Simplify
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
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt14
Bruce Mayer, PE Chabot College Mathematics
Example Example Simplify Simplify
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
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt15
Bruce Mayer, PE Chabot College Mathematics
Example Example Simplify Simplify
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
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt16
Bruce Mayer, PE Chabot College Mathematics
Example Example Simplify Simplify
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
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt17
Bruce Mayer, PE Chabot College Mathematics
WhiteBoard WorkWhiteBoard Work
Problems From §7.3 Exercise Set• 76, 80, 82, 92, 98
AdultCardiacIndex =2.8-3.4
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt18
Bruce Mayer, PE Chabot College Mathematics
All Done for TodayAll Done for Today
ExponentRules are
NOTAlgebraic
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt19
Bruce Mayer, PE Chabot College Mathematics
Bruce Mayer, PELicensed Electrical & Mechanical Engineer
Chabot Mathematics
AppendiAppendixx
–
srsrsr 22
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt20
Bruce Mayer, PE Chabot College Mathematics
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
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-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
file =XY_Plot_0211.xls
[email protected] • MTH55_Lec-42_sec_7-3b_Factor_Radicals.ppt21
Bruce Mayer, PE Chabot College Mathematics
-3
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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
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