7­2 multiplying and dividing radicals web.notebook
February 03, 2009
7­2
Multiplying and Dividing Radical Expressions
Objective: To multiply radical expressions
To divide radical expressions
Dec 21­9:30 AM
Multiplying radical expressions
Dec 21­9:30 AM
Multiply. Simplify if possible.
.
Ex: √3 √12
.
.
Ex: ∛-16 ∛4
Ex: √-4 √16
*Same root
Dec 21­9:30 AM
Simplifying radical expressions
Dec 21­9:30 AM
Multiplying and simplify the radical expressions.
Ex: ∛25xy8
Ex: √72x
3
. ∛5x y
4 3
Ex: ∛80n5
Dec 21­9:30 AM
Dec 21­9:30 AM
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7­2 multiplying and dividing radicals web.notebook
February 03, 2009
Multiplying and simplify the radical expressions.
Dividing Radical Expressions
.
Ex: 3√7x3 2√21x3y2
*Same root
Dec 21­9:30 AM
Dec 21­9:30 AM
Example #2: Divide and simplify. Assume that all variables are positive.
Example #1: Divide and simplify. Assume that all varaibles are positive.
a.
√243
√27
4
b.
√12x
√3x
c.
∜1024x
∜4x
15
a. ∛32 32
= 3
∛­4 ­4 = ∛­8 = ­2 √
b. ∛162x5 162x5 . . 3 = 3x∛2
= 3
= ∛54x3 = ∛27 2 x
2
∛3x2 3x
√
Dec 21­9:30 AM
Dec 21­9:30 AM
To rationalize the denominator of an expression, rewrite it so there are no radicals in any denominator and no denominators in any radical. This makes it easier to calculate the decimal approximation.
Example:
Jan 29­8:57 AM
1 √2 Dec 21­9:30 AM
2
7­2 multiplying and dividing radicals web.notebook
February 03, 2009
Example #3: (continued)
Example #3: Rationalize the denominator of each expression. Assume that all variables are positive.
3
b. √x =
√5xy a. √2
√3
6
√2 = √2 √3 =√
√3 √3 √3 3
c. *Multiply the numerator and denominator by √3 so the denominator becomes a whole number.
2 =
√ 3x 3
*Rewrite the fraction so the denominator is a perfect cube.
Dec 21­9:30 AM
Dec 21­9:30 AM
Example #4: Rationalize the denominator of each expression. Assume that all variables are positive.
a.
7
5
√
b. √2x
3
√10xy
c.
∛4
∛6x
Example #5: Einstein's famous formula E = mc2 relates energy E, mass m, and the speed of light c. Express c in terms of E and m and rationalize the denominator.
E = mc2
c2 = E
m
c = Dec 21­9:30 AM
E Em √Em √Em
=
=
=
√m m
√m m
√ 2
2
Dec 21­9:30 AM
Homework
Practice 7.2
Dec 21­9:30 AM
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