9-4 Simplifying Radicals
Objective: Simplify radicals involving products and
quotients.
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Warm Up
Find each value.
√4
√144
RADICALS √
3√25
-3√49
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Perfect Squares
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A radical expression is in simplest form when all three
statements are true.
1. The expression under the radical sign has no perfect
square factors other than 1.
2. The expression under the radical sign does not contain
a fraction.
3. The denominator does not contain a radical expression.
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Multiplication Property of Square Roots
For any numbers a ≥ 0 and b ≥ 0,
√ab = √a•√b .
Example:
√54
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To simplify a radical, "take out" from
under the radical sign the largest
perfect square factor contained within
the radicand.
6
Simplify each radical expression.
√8
√75
√50
√18
√192
√320
7
If you cannot easily see the largest
perfect square factor in the radicand,
use the prime factorization method.
Example:
√150
1. Factor
2. Find the perfect square pairs.
3. "Take out" from under
the radical sign the square
root of each perfect square.
8
Simplify each radical expression.
√6•√15
5√300
√13•√52
Note:
√7•√7
√5•√5
√3•√3
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Division Property of Square Roots
For any numbers a ≥ 0 and b > 0,
=
Example:
10
Simplify each radical expression.
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HW # 107
p. 433 # 6 ­ 20 even, 26 ­ 34 even
** Copy problem and simplify.
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