Chapter 2 notes
2A Rational and Irrational n u m b e rs
Rational, Irritational numbers and s u rd s
Rational -
, 2.9, 1.6
Irrational -> B, 5,2π
-
3
surds ->
5,5x, 1 55.
+
Rules
thatapply to Surds
- -
fiz 2
52
·
(5)2 and i
when, (5) 3
= =
x =
=
⑤
is men o
Ic x y
=
0 >, ⑧ 6 X 2
when x >, and y
-
-
·w ana a
3
simplifying s u rd s
92 x b =
a2x D 52 =
16 2
+
-
ar
b
=
42 2
x
=Fr x
45
=
2
2B
Adding and Subtracting Surds
->
simplify all surds before attempting to addo r them
subtract
Example of adding and
subtracting surds
255 -
3520 6/45
+
255
=
-
35
6xx5
+
Step one ->
Simplify the s u rd s by splitting into
common factors
1855
=
255 -
65 +
Step
2 > write o u tt h e
fully
--
simplified equation
1455 Step
=
3
complete
->
the eavation by fathering like
-
erms
, chapter 2n o te s
2C Multiplying and
Dividing Surds
Rules For
Multiplying and Dividing Surds
When multiplying surds:
·
( 5
x
Xxy
=
·
a x by =
aby
When dividing surds:
= =I
E
·
a
·
when expanding b r acke ts , use the distributive
l aw
-
-
·
a(b c) +
=
ab ac,soE(5
+
1)
+
=
5 E
+
Example of Distributive L aw
30(240 -
45)
Step one -> Expand the equation by using the distributive
05
= -
1256 a w
ste p t wo -> simplify splitting surds into
6xis by the common
=
12 6
x
-
factors
1255 72 Step t h re e
writting
=
-
-
complete by fully simplified eq
2D Binomial Produc ts
Distributive l aw
(a +
b)(c d) +
=
ac ad
+
bc
+ bd
+
Expanding Per fec t
s q u a re s
(a +
b)2 =
(a b)(a +
b)
+
(E 1)
+
(Ez 1)(- 1)
=
+
+
q2 b2 E
=
I ab ba 2 E 1
+ + +
+ + +
q2 2ab b2
+
2
3
= + =
-
(a b)2 (a b)(a b) 1)
(12 1)(E
-
= -
- - -
a2
=
-
ab -
ba b2
+
=2 -
5 -
I 1
+
a 2ab b2
2
=
= 3
- +
-
Forming a difference of
t wo squares
(a b)(a
+
-
b) az
= -
ab ba
+ b2
+ (2 +
1)(5 -
1) =
2
-
5 2
+
-
1
- q2 -
b2 -
2 -
1
=
I
2A Rational and Irrational n u m b e rs
Rational, Irritational numbers and s u rd s
Rational -
, 2.9, 1.6
Irrational -> B, 5,2π
-
3
surds ->
5,5x, 1 55.
+
Rules
thatapply to Surds
- -
fiz 2
52
·
(5)2 and i
when, (5) 3
= =
x =
=
⑤
is men o
Ic x y
=
0 >, ⑧ 6 X 2
when x >, and y
-
-
·w ana a
3
simplifying s u rd s
92 x b =
a2x D 52 =
16 2
+
-
ar
b
=
42 2
x
=Fr x
45
=
2
2B
Adding and Subtracting Surds
->
simplify all surds before attempting to addo r them
subtract
Example of adding and
subtracting surds
255 -
3520 6/45
+
255
=
-
35
6xx5
+
Step one ->
Simplify the s u rd s by splitting into
common factors
1855
=
255 -
65 +
Step
2 > write o u tt h e
fully
--
simplified equation
1455 Step
=
3
complete
->
the eavation by fathering like
-
erms
, chapter 2n o te s
2C Multiplying and
Dividing Surds
Rules For
Multiplying and Dividing Surds
When multiplying surds:
·
( 5
x
Xxy
=
·
a x by =
aby
When dividing surds:
= =I
E
·
a
·
when expanding b r acke ts , use the distributive
l aw
-
-
·
a(b c) +
=
ab ac,soE(5
+
1)
+
=
5 E
+
Example of Distributive L aw
30(240 -
45)
Step one -> Expand the equation by using the distributive
05
= -
1256 a w
ste p t wo -> simplify splitting surds into
6xis by the common
=
12 6
x
-
factors
1255 72 Step t h re e
writting
=
-
-
complete by fully simplified eq
2D Binomial Produc ts
Distributive l aw
(a +
b)(c d) +
=
ac ad
+
bc
+ bd
+
Expanding Per fec t
s q u a re s
(a +
b)2 =
(a b)(a +
b)
+
(E 1)
+
(Ez 1)(- 1)
=
+
+
q2 b2 E
=
I ab ba 2 E 1
+ + +
+ + +
q2 2ab b2
+
2
3
= + =
-
(a b)2 (a b)(a b) 1)
(12 1)(E
-
= -
- - -
a2
=
-
ab -
ba b2
+
=2 -
5 -
I 1
+
a 2ab b2
2
=
= 3
- +
-
Forming a difference of
t wo squares
(a b)(a
+
-
b) az
= -
ab ba
+ b2
+ (2 +
1)(5 -
1) =
2
-
5 2
+
-
1
- q2 -
b2 -
2 -
1
=
I
