
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt
Chabot College Mathematics
1

Review § 7.3
MTH 55
 Any QUESTIONS About
• §7.3 → Multiply Radicals
 Any QUESTIONS About HomeWork
• §7.3 → HW-32
Chabot College Mathematics
2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt

Add & Subtract Radicals
 Radical Expressions similar to those that follow can be simplified using the distributive property
These canNOT be combined
Chabot College Mathematics
3
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt

CAVEAT Identical Indices
 CAUTION
 Only Radical Expressions with the
SAME INDEX and SAME RADICAND may be combined
 Expressions such as Those below
CanNOT be simplified by Combining
Terms
Chabot College Mathematics
4
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt

Example

Simplify by Add/Sub
 Simplify by Adding or Subtracting a) b)
 SOLN → chk 1 st Indices & Radicands a) b)
Chabot College Mathematics
5
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt

Example

Simplify by Add/Sub
 Simplify by Adding or Subtracting a)
28

7 b)
63

112

28
 SOLN → chk 1 st Indices & Radicands a) 28

7

4 7 7

2 7

7

3 7
Factor 28.
Simplify Radical
Combine like radicals.
b)
63

112

28

9 7 16 7 4 7
Chabot College Mathematics
6

3 7

4 7

2 7
 
3 7
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt

Example

Simplify by Add/Sub
 Simplify by Adding or Subtracting a)
7 5 x

12 5 x b) 14 5
 
 SOLN → chk 1 st Indices & Radicands
Combine the like radicals by a)
7 5 x

12 5 x
 
5 5 x subtracting the coefficients and keeping the radical.
b) 14 5
 

(14 5) 5
 

9 5

11
Chabot College Mathematics
7
Regroup terms.
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt

Example

Simplify by Add/Sub
 Simplify by Adding or Subtracting
 SOLN → chk 1 st Indices & Radicands
Chabot College Mathematics
8
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt

Example

Simplify by Add/Sub
 Simplify by Adding or Subtracting
(assume a , b > 0)
 SOLN → Note that these are CUBE Rts
Chabot College Mathematics
9
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt

Radical 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.
Chabot College Mathematics
10
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt

Quotient Rule for Radicals
 a a with b > 0 n a
 n a b n b
.
and n n
,

0,
 Remember that an n th root is simplified when its radicand has no factors that are perfect n th pwrs
• Recall also that we assume that no radicands represent negative quantities raised to an even power
Chabot College Mathematics
11
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt

Example

Simplify by Quotient
 Simplify by taking roots of the a) x
49 x
4 a)
 SOLN a) b)
4 n
3
49

49 x
4 x
4

7 x
2
3
54 m
4 n
3
Taking the square roots of the numerator & denominator
Chabot College Mathematics
12
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt

Example

Simplify by Quotient
 Simplify by taking roots of b) 3
54 m
4 n
3 the numerator a)
& denominator:

3
54 m
4

3   m
3  m
3
54 m
4 n
3

3
27 m

2 m
 SOLN b) →
Chabot College Mathematics
13

3 m
3
2 m n
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt

WhiteBoard Work
 Problems From §7.4 Exercise Set
• 10, 26, 28, 40, 56, 60, 84
 Recall Σ & Δ of Two Cubes
• DIFFERENCE of Cubes:
• a ³ − b ³ = ( a − b )( a ² + ab + b ²)
• SUM of Cubes:
• a ³ + b ³ = ( a + b )( a ² − ab + b ²)
Chabot College Mathematics
14
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt

All Done for Today
 Born March 14, 1879 in Ulm, Württemberg,
Germany
Chabot College Mathematics
15
 Died April 18, 1955 (age
76) in Princeton, New
Jersey, USA
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt

r
2  s
2 
 r
 s
 r
 s

Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
–
Chabot College Mathematics
16
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt

Graph y = |x|
6
 Make T-table
y = |x | x
5
6
3
4
-1
0
1
2
-6
-5
-4
-3
-2
5
6
3
4
1
2
1
0
4
3
6
5
2
5
4
3
2
1
-6 -5 -4 -3 -2 -1
0
-1
0
-2
-3
-4
-5
Chabot College Mathematics
17 y
1 2 3
-6 file =XY_Plot_0211.xls
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt
4 5 x
6

-3 -2
2
1
-1
0
0
-1
-2
M55_§JBerland_Graphs_0806.xls
-3
5
4
3
1
4
5 y
2
-10 -8
3
3
2
-6
4
-4
5
1
-2
0
0
-1
-2
M55_§JBerland_Graphs_0806.xls
-3
-4
-5
2 4 6 8 x
10
Chabot College Mathematics
18
Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH55_Lec-43_sec_7-4_Add_Sub_Divide_Radicals.ppt