MATD 0390 Intermediate Algebra
Christy Dittmar
Section 6.3 notes: Simplifying Radical Expressions Using Laws of Radicals
Simplifying Radical Expressions Using Laws of Radicals (6.3)
Product Property of Radicals
If
n
a and
n
b are real numbers, and n ! 2 is an integer, then
n
a ! n b = n ab
5 ! 20
4
x5 ! 4 x7
9
10s ! 9 5s 7
Simplifying radicals using the product property Rewrite the expression as a product of a perfect power and a remainder.
20
3
40
3
y14
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MATD 0390 Intermediate Algebra
Christy Dittmar
Section 6.3 notes: Simplifying Radical Expressions Using Laws of Radicals
45x 6
3
!54x 3 y 7
4
48a 3b 8
c7
4 ! 24
2
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MATD 0390 Intermediate Algebra
Christy Dittmar
Section 6.3 notes: Simplifying Radical Expressions Using Laws of Radicals
Multiply and simplify. 7x 3 ! 14x 6
5
8x 4 y ! 5 4x13 y 4
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MATD 0390 Intermediate Algebra
Christy Dittmar
Section 6.3 notes: Simplifying Radical Expressions Using Laws of Radicals
Quotient Property of Radicals
If
n
a and
n
b are real numbers, and n ! 2 is an integer, then
n
n
a
=
b
n
a
b
Divide and simplify. 108
3
3
108a 8b
3
2ab 5
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