Simplifying Radicals
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Simplifying Radicals Topic: Radical Expressions Essential Question: How are radical expressions represented and how can you solve them?
description
Topic: Radical Expressions Essential Question: How are radical expressions represented and how can you solve them?. Simplifying Radicals. What numbers are perfect squares?. 1 • 1 = 1 2 • 2 = 4 3 • 3 = 9 4 • 4 = 16 5 • 5 = 25 6 • 6 = 36 - PowerPoint PPT Presentation
Transcript of Simplifying Radicals
Simplifying Radicals
Topic: Radical ExpressionsEssential Question: How are radical expressions represented and how can you solve them?
1 • 1 = 12 • 2 = 43 • 3 = 9
4 • 4 = 165 • 5 = 256 • 6 = 36
49, 64, 81, 100, 121, 144, ...
What numbers are perfect squares?
A List of Some Perfect Squares
1
4
916
253649
64
81
100121
144169196
225
256
324
400
625
289
4
16
25
100
144
= 2
= 4
= 5
= 10
= 12
That was easy!
8
20
32
75
40
=
= =
=
=
2*4
5*4
2*16
3*25
10*4
=
=
=
=
=
22
52
24
35
102
Perfect Square Factor * Other Factor
LE
AV
E I
N R
AD
ICA
L F
OR
M
48
80
50
125
450
=
= =
=
=
3*16
5*16
2*25
5*25
2*225
=
=
=
=
=
34
54
25
55
215
Perfect Square Factor * Other Factor
LE
AV
E I
N R
AD
ICA
L F
OR
M
1. Simplify 147
Simplify
1. .
2. .
3. .
4. .
2 18
72
3 8
6 236 2
+To combine radicals: combine the coefficients of like radicals
Hint: In order to combine radicals they must be like terms
Simplify each expression
737576 78
62747365 7763
Simplify each expression: Simplify each radical first and then combine.
323502
22
212210
24*325*2
2*1632*252
Simplify each expression: Simplify each radical first and then combine.
485273
329
32039
34*533*3
3*1653*93
Simplify each expression
636556
547243
32782
Simplify each expression
20556
32718
6367282
*To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.
Hint: to multiply radicals they DO NOT need to be like terms
35*5 175 7*25 75
Multiply and then simplify
73*82 566 14*46
142*6 1412
204*52 1008 8010*8
2
5 5*5 25 5
2
7 7*7 49 7
To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator
7
56 8 2*4 22
Simplify
108
3
108
3
36
6
Uh oh…There is a
radical in the denominator!
Whew! It simplified!
Simplify
8 2
2 8
4 1
4
4
2
2
Uh oh…Another radical
in the denominator!
Whew! It simplified again! I hope they all are
like this!
7
6This cannot be
divided which leaves the radical in the
denominator. We do not leave radicals in the denominator. So
we need to rationalize by multiplying the
fraction by something so we can eliminate
the radical in the denominator.
7
7*
7
6
49
42
7
42
42 cannot be simplified, so we are
finished.
Simplify
5
7
5
7
35
49 35
7
Since the fraction doesn’t reduce, split the radical up.
Uh oh…There is a
fraction in the radical!
How do I get rid of the radical in the
denominator?
Multiply by the “fancy one” to make the denominator a perfect
square!
This can be divided which leaves the
radical in the denominator. We do not leave radicals in the denominator. So
we need to rationalize by multiplying the
fraction by something so we can eliminate
the radical in the denominator.
10
5
2
2*
2
1
2
2
This cannot be divided which leaves
the radical in the denominator. We do not leave radicals in the denominator. So
we need to rationalize by multiplying the
fraction by something so we can eliminate
the radical in the denominator.
12
3
3
3*
12
3
36
33
6
33
2
3Reduce
the fraction.
2X
6Y
264 YXP
244 YX
10825 DC
= X
= Y3
= P2X3Y
= 2X2Y
= 5C4D5
3X
XX
=
=
XX *2
YY 45Y
=
= YY 2
Simplify
1. .
2. .
3. .
4. .
24 3x44 3x
2 48x448x
(3 6 2 3)(4 3)
3 6F
4 3 6O
3 2 3I
4 2 3L
3
12 6 3 32 2 8 3 2 3
12 6 9 2 8 3 6
Since there are no like terms, you can not combine.
Challenge:
How do you know when a radical problem is done?
1. No radicals can be simplified.Example:
2. There are no fractions in the radical.Example:
3. There are no radicals in the denominator.Example:
8
1
4
1
5
