multiplying, dividing, and simplifying radicals 10.3 1.multiply radical expressions. 2.divide...
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Multiplying, Dividing, and Simplifying Radicals10.310.3
1. Multiply radical expressions.2. Divide radical expressions.3. Use the product rule to simplify radical expressions.
254 1052 100 10
Product Rule for Radicals
If both and are real numbers, then
.n n na b a b
n a n b
The index (root) must be the same!
2516
54
2516
54
The index (root) must be the same!
, where 0.n
nn
a ab
bb
Quotient Rule for RadicalsIf both and are real numbers, thenn a n b
149162536496481100
Simplify radicals:Simplify radicals:
20 54 52
Look for the largest perfect square that divides into the radicand evenly.
54
75 325 35325
60 154 152154
48 316 34316
Simplify radicals:Simplify radicals:
3x xxxxx
5x xxx xxxxx
xx2
1132R
Outsid
e
Insid
e
1252R
Outsid
e
Insid
e
Think…
Simplify:Simplify:
3 52724 zyx 3 53 23 73 24 zyx
3
8∙3
3 32 xx 32 2 3 22 32 xyx
2153R12
73R 20
23R
3 222 32 zxyzx
Simplify:Simplify:46
109
59
24054
sr
sr
46
109
5240
954
srsr
63486 sr16∙3
rr 346 346
149162536496481100
rrs 324 3
6 rrs 346 3
Slide 10- 27Copyright © 2011 Pearson Education, Inc.
Simplify.
a)
b)
c)
d)
2 33 9m m
3 3m m
23 3m m
627m
2 33 3m m
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