Section 6.6 Division of Radicals
HOMEWORK: Sec 6.6: 1 – 25 odd, 35 – 51 odd, 57 - 87 odd
Definition of Simplified Radical Form
A radical expression where the radicand is written as a product
of prime factors is in simplified form if ALL of the following
conditions are met:
1. The radicand has no factors raised to a power greater than
the power of the index.
2. The radicand does not contain a fraction
3. There are no radicals in the denominator of a fraction.
Multiplication Property of Radicals
Let a and b represent real numbers such that
n
a and b are
n
a
a

b0
b
b
n
both real. Then
n
n
Page 1
Section 6.6 Division of Radicals
Example: Simplify
3
Simplify
3
48s
2s
16 x
25 y
5
6
8
3
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Section 6.6 Division of Radicals
Rationalizing the denominator:
One term: Multiply by a radical to create an nth root of an
nth power.
Two Terms: Multiply by the conjugate.
Rationalize
3
4
x
10
Simplify
2x
4
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Section 6.6 Division of Radicals
5
Simplify
8x
3y
Simplify
6
3x
3
2
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Section 6.6 Division of Radicals
Simplify
Simplify
3
2 5
2 y
2 y
Page 5
Section 6.6 Division of Radicals
3 x
Simplify
1 x
Additional Examples:
Page 6