[email protected] MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 1 Bruce Mayer, PE Chabot College Mathematics Bruce Mayer, PE Licensed Electrical

[email protected] • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt1

Bruce Mayer, PE Chabot College Mathematics

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Chabot Mathematics

§7.4 +/§7.4 +/−/−/RadicalsRadicals



Review §Review §

Any QUESTIONS About• §7.3 → Multiply Radicals

Any QUESTIONS About HomeWork• §7.3 → HW-26

7.3 MTH 55



Add & Subtract RadicalsAdd & Subtract Radicals

Radical Expressions similar to those that follow can be simplified using the distributive property

These canNOT be combined



CAVEAT Identical IndicesCAVEAT Identical Indices

CAUTIONCAUTION Only Radical Expressions with the

SAME INDEX and SAME RADICAND may be combined

Expressions such as Those below CanNOT be simplified by Combining Terms



Example Example Simplify by Add/Sub Simplify by Add/Sub

Simplify by Adding or Subtractinga) b)

SOLN → chk 1st Indices & Radicands a) b)





SOLN → chk 1st Indices & Radicandsa)

28 7 63 112 28

4 7 7 Factor 28.28 7

2 7 7 3 7 Combine like radicals.

Simplify Radical

b) 63 112 28 9 7 16 7 4 7

3 7 4 7 2 7

3 7





SOLN → chk 1st Indices & Radicandsa)

b)

14 5 11 2 11 5 5

3 37 5 12 5x x 35 5xCombine the like radicals by subtracting the coefficients and keeping the radical.

14 5 11 2 11 5 5

(14 5) 5 (2 1) 11

9 5 11

Regroup terms.

3 37 5 12 5x x




Simplify by Adding or Subtracting

SOLN → chk 1st Indices & Radicands




Simplify by Adding or Subtracting (assume a, b > 0)

SOLN → Note that these are CUBE Rts



Radical Expression DivisionRadical Expression Division

Just as the root of a product can be expressed as the product of two roots, the root of a quotient can be expressed as the quotient of two roots.



Quotient Rule for RadicalsQuotient Rule for Radicals

For any real numbers andwith b > 0

Remember that an nth root is simplified when its radicand has no factors that are perfect nth pwrs • Recall also that we assume that no radicands

represent negative quantities raised to an even power



Example Example Simplify by Quotient Simplify by Quotient

Simplify by taking roots of the numerator and denominator:

a) b)

SOLN a)

27

x Taking the square roots of the

numerator & denominator



Example Example Simplify by Quotient Simplify by Quotient

Simplify by taking roots of the numerator & denominator:

b)

SOLN b) →

3 3

3 3

27 2 m m

n

3 3 3

3 3

27 2m m

n

33 2m m

n



WhiteBoard WorkWhiteBoard Work

Problems From §7.4 Exercise Set• 10, 26, 28, 40, 56, 60, 84

Recall Σ & Δ of Two Cubes• DIFFERENCE of Cubes:

• a³ − b³ = (a − b)(a² + ab + b²)

• SUM of Cubes:

• a³ + b³ = (a + b)(a² − ab + b²)



All Done for TodayAll Done for Today

AlbertEinstein

Born March 14, 1879 in Ulm, Württemberg, Germany

Died April 18, 1955 (age 76) in Princeton, New Jersey, USA



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

2

3

4

5

6

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

file =XY_Plot_0211.xls



-3

-2

-1

0

1

2

3

4

5

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

M55_§JBerland_Graphs_0806.xls -5

-4

-3

-2

-1

0

1

2

3

4

5

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

M55_§JBerland_Graphs_0806.xls

x

y

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[email protected] MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt 1 Bruce Mayer, PE Chabot College Mathematics Bruce Mayer, PE Licensed Electrical