Download Radical Expressions and Equations

Radical Expressions and Equations
The Mechanics: Operations with Radical Expressions
nitians:
)
5
q
• I ike Radicals: have the same radicand, (Lx: 55 4
• Unlike Radicats: do not have the same radicand. (Lx: 4s 5, 3 \6)
When adding/subtracting radical expressions:
1. Simplify Radical Expressions
2. Combine Like Radicals
• Add/Subtract the numbers outside of radicand.
• Radicand stays the same
esombiLike Radicals
Simplify
1. 232
Step 1: Simplify the radicals
Both ‘v2 and 3\2 are simplified
Step 2: Group like terms (i.e like radicatids)
(1 ±3)J2
Step 3: Simplify
Note: Radicand of 2 staved the same
2. 42+8
Step 1: Simplify the radicals
42 is already simplified
Step 2: Group like terms (Lee like radleands)
(4 + 2)2
Step 3: Simplify
6J2
Note: Radicand of2 stayed the same
iceçbininLikeRajcals
Simplify
a. 3J5 45
b. 4J3
The Mechanics: Radical Operations
+
3
c.
IC) 5iO
d 7’3 12
Radical Expressions and Equations
utiveroert
r with all radicals.
When applying distributive property, make sure o multiph numbe
Examples:
\/(3 *f) + 73
8 + 73
1
q
*
2) + 73
3 2 73
Use distributl\e property
Multiply
I actor radicands
pull out pcrfectsquares
Add like terms (cant combine 3’ 2
2
q
3
Practice: Applying Distributive Property
b \2x(&x Ii)
a ‘‘5(2 I0)
c. \5a(5a
Qiions:1ultilinierms
73)
3)
Foil or box method can be used when multiplying 2 radical terms.
Examples: Multiplying 2 Terms
Method 1: Foil
(5 2J15) (5
±
l5)
-
‘15 215*5 215*ul5
25 75-2’752?’5
5 (i2)i752*[5
30
5 \175
30
5
-25 5’3
—
Method 2: Box
15
‘J
215
[*215
H
q75
L
=5-275 4 75-30
(530) (2l)’75
i75
= 25
.q
5
3
-25
—
Shortcuts:
±b
b)
2ab
ai-+
(a
=
2
2
2 b
(a + b)(a-b) = a
-
The Mechanics Radical Operations
List all tcrms from box
Combine like terms
Subtract
Simplify radicands
d. 3I2(7
4J5)
Radical Expressions and Equations
Practice: Multiplying 2 Terms.
a. (26 3I3)(6
-
+
53)
b. (6 32l)6
+
21)
c. (7
4)2
d. (2lO
9!ions:nuates
Conjugates are sum & difference of the same 2 terms.
Product of 2 conjugates results in difference of 2 squares.
Exam les: Co&u ates
,I5 +
‘2 and 5
‘i2 are conjugates of each other
Their product will be
(5 + J2)(’J5 ‘J2) =
—
-
(2)2
term squared 2 term squared
No radical in answer
—
5
2
=
3
ice:1dent1uItiIvConuates
Identify and multiply each radical expression with its conjugate
a5-2
b’8±9
c7+5
dlO±8
ions:Rationa1izin Denominators
When denominator contains sum/difference including radical expressions, rationa
lize
denominator by multiplying numerator & denominator by conjugate of denominator.
Examples:
6
6
Identify the conjugate of denominator: ‘5
*
5+2
2
÷
5
j
q
+
Multiply both numerator & denominator by: 5
Simplify
=
-
2)(5
+
2)
(5)2
—2’2
(‘2) 2
The Mechanics: Radical Operations
5-2
3
3
+
± 3)2
Radical Expressions and Equations
.•
Practice: Rationalizing the Denominator
a. 4
(11O + 48)
(47 + 45)
C.
8
iti
(411-93)
(*-93)
e. 3-’16
£
(5- 296)
The Mechanics: Radical Operations
4
42
(96-3)