Transcript 12.2 adding subtracting radicals

Warm-up
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Simplify the following square roots.
1.
85a b c
4
5
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2.
225a16b2
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3.
34b
answers :
2 2
ab
15a 8b
34b
85bc
Homework Answers
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18. 6/7
20. 6/5
22. -1/8
24. -10
26. -5/3
28. 10
30. -6, 9
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14. 255
16. 416
18. $262.50
20. 170.4 mi
22. $160
24. 275%
26. 15%
Operations with Radical
Expression
Section 12.2
Essential Question
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How do I add and subtract radical
expressions?
How do I use FOIL and the distributive
property with radicals?
Add/Subtract Radicals
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In order to add/subtract expressions that
contain radicals, the radicands MUST
be identical . . . Aka. LIKE TERMS!
Remember:
5x + 2x = 7x
So . . .
Treat the radical
just like you would
treat a variable.
5 32 3 7 3
Can you add non-like terms?
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For instance: 4x + 3y
NO!
Likewise, you cannot add radicals w/
different radicands.
3 2 4 5
Cannot add!
Leave like it is.
You try.
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Add /Subtract.
Answers!
1. 5 6  2 6
3 6
2. 5  6 7  2 7  3
24 7
3. 8 3  6 2  3  2 2
7 3 8 2
4. a x  b x
(a  b ) x
What if the radicands aren’t =?
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Simplify all square roots first to see if the radicands
are the same.
For example: 5 28  6 48  10 12
 5 2  2  7  6 2  2  2  2  3  10 2  2  3
 10 7  24 3  20 3
 10 7  4 3
You Try!
Add.
80  98  128
4 5 7 2 8 2
4 5  15 2
Distribute.
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Multiply/distribute.
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2 6  12
This is
simplified.
Can’t add.
Radicands are
different.
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6 2  24
6 2  2 2 23
6 2 2 6
Use FOIL
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Multiply.
(3  2 )( 4  2 )
F irst
O utside
12  3 2  4 2  2
I nside
L ast
10  2
Always write number term before radical term!
Conjugates
Expression
Conjugate
Product
a b
a b
a b
4 x
4 x
16  x
c 2
c 2
c 2
y 7
y 7
y 7
2
2
2
Example
3
4 2
3
4 2
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4 2 4 2
12  3 2
16  2
3(4  2 )
4  2 (4  2 )
12  3 2
14
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Classwork
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Page 144
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Numbers 19 – 26 all
Homwork
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Page 145
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Numbers 16 – 26 all
Summarizer
A common mistake people make is to tell me that
2 5  2 5  4 10
Why is this not true?
Be sure to NOT do that because . . .
2 5  2 5  4 10