Transcript Slide 1

Simplifying Radical
Expressions
MATH 018
Combined Algebra
S. Rook
Overview
• Section 10.3 in the textbook:
– Applying the product rule for radicals
– Applying the quotient rule for radicals
– Simplifying radicals
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Product Rule for Radicals
Product Rule for Radicals
• Used when multiplying two radicals with the
same root index
n
a  n b  n a b
• Simplify the final result if possible
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Product Rule for Radicals
(Example)
Ex 1: Simplify:
32  2
a)
b)
c)
3
9a  3 3a
2
5a  3a
5
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Quotient Rule For Radicals
Quotient Rule for Radicals
• Used to split apart a fraction under one root
index into a quotient of the same root index
n
a na
n
b
b
• Simplify the numerator and denominator of
the final result if possible
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Quotient Rule for Radicals
(Example)
Ex 2: Simplify:
64
8
x
a)
b)
3
64
9
b
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Simplifying Radicals
Simplifying Radicals
• Goal is to separate into 2 radicals
– Perfect radical comprised of perfect roots
– Miscellaneous radical
• We do this by reversing the product rule
• Consider simplifying 8
– What is the root index?
– This means that we are looking for the largest
perfect _____ that will evenly divide into 8 which
is…
– What should go into the miscellaneous radical
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according to the product rule?
Simplifying Radicals (Example)
Ex 3: Simplify:
a)
24
d)
3
16
b)
80
e)
3
108
c)
27
f)
3
40
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Simplify Radicals (Example)
Ex 4: Simplify:
a)
18a b c
b)
28ab15c23
c)
6 9
3
54a 2b17 c15
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Summary
• After studying these slides, you should know
how to do the following:
– Apply the product rule when multiplying two radicals
with the same index
– Apply the quotient rule when dividing two radicals with
the same index
– Simplify a radical expression
• Additional Practice
– See the list of suggested problems for 10.3
• Next lesson
– Adding, Subtracting, and Multiplying Radical
Expressions (Section 10.4)
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