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Transcript of = 2 = 4 = 5 = 10 = 12 Simplify. Objective - To simplify rational and irrational square roots. List...
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4
16
25
100
144
= 2
= 4
= 5= 10
= 12
Simplify
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Objective - To simplify rational and irrational square roots.
List of Perfect Squares
3649
64
81
100
121
67891011
144
169
196
225
400
625
121314152025
256 16
289 17
324 18
361 19
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Objective - To simplify irrational roots.
Example:
Check using a calculator!
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Simplify.
To simplify the number by hand must have a perfect square factor.
No perfectsquare factors Can’t be
simplified
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1)
2)
3)
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5)
6)
Simplify each irrational root.
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Simplify.
Perfect square
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Simplify each irrational root.
1)
2)
3)
4)
5)
6)80 16 5 16 5 4 5
Already Simplified
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Ex. 1 Simplify
40 75 32
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450 50 80
Ex. 2 Simplify
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To simplify radicals with variables: divide even exponents by 2; for odd exponents, pull out the largest even exponent, take the square root of that, and leave the remainder under the radical.
Radicals with Variables
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Radicals with VariablesEx. 10 Even
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Radicals with VariablesEx. 11 Odd
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+To combine radicals: combine the coefficients of like radicals. They must have the same last name.
Combine Like Radicals
Miller Miller
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78
62747365 7763
737576
Ex. 3 Simplify
636556
Your Turn
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Simplify, then combine.
485273
Ex. 4
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Simplify, then combine.Ex. 5
547243
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Slide 10- 17
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example496 .a b
416 6 a b
416 6a b
24 6 a b
The greatest perfect square factor of 96a4b is 16a4.
Use the product rule of square roots to separate the factors into two radicals.
Find the square root of 16a4 and leave 6b in the radical.
496a b
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Slide 10- 18
Example
Solution
532x
416 2x x
24 2 x x
532x The greatest perfect square factor of 32x5 is 16x4.
Use the product rule of square roots to separate the factors into two radicals.
Find the square root of 16x4 and leave 2x in the radical.
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To multiply radicals: multiply everything, then simplify.
Multiply Radicals
*
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35*5
Ex. 6
204*52
Multiply, then simplify.
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2
7
2
8
2
x
Squared and Square Root Cancel
Ex. 7
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To divide radicals: reduce or divide what you can and rationalize the denominator. A square root CANNOT be in the denominator.
Dividing Radicals
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7
56
7
6
10
5
Ex. 8 Reduce or divide, then
rationalize.
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Ex. 9
12
3