7­2 Day 2 Dividing Radical Expressions
January 30, 2009
7­2 Day 2 ­ Dividing Radical Expressions
Objective: Divide radical expressions.
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7­2 Day 2 Dividing Radical Expressions
January 30, 2009
Simplify each of the following expressions and look for a pattern.
√36 6
=
√25 5
√( )
2
36 6 6
=
=
25 5 5
√
Therefore, √36 36
=
√25 25 .
√
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7­2 Day 2 Dividing Radical Expressions
January 30, 2009
Dividing Radical Expressions
*Same root
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7­2 Day 2 Dividing Radical Expressions
January 30, 2009
Example #1: Divide and simplify. Assume that all varaibles are positive.
a. ∛32 32
= 3
∛­4 ­4 = ∛­8 = ­2 √
b. ∛162x5 162x5 = ∛54x3 = ∛27x3(2) = 3x∛2
2 = 3
2
∛3x 3x √
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7­2 Day 2 Dividing Radical Expressions
January 30, 2009
Example #2: Divide and simplify. Assume that all variables are positive.
a.
√243
√27
4
b.
√12x
√3x
c.
∜1024x
∜4x
15
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7­2 Day 2 Dividing Radical Expressions
January 30, 2009
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:
1 √2
=
√2 2
*Two methods of rationalizing the denominator are shown on the next page.
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7­2 Day 2 Dividing Radical Expressions
January 30, 2009
Example #3: Rationalize the denominator of each expression. Assume that all variables are positive.
a. √2
√3
Method 1
√2 2 2 3 6 √6 √6
=
=
=
=
2
2 =
√3 3 3 3 3 √3 3
√ √
√
*Rewrite as a square root of a fraction. Then make the denominator a perfect square.
Method 2
6
√2 = √2 √3 =√
√3 √3 √3 3
*Multiply the numerator and denominator by √3 so the denominator becomes a whole number.
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7­2 Day 2 Dividing Radical Expressions
January 30, 2009
Example #3: (continued)
x3 √5xy √5x4y x2√5y x√5y
b. √x3 √
=
=
=
=
√5xy √5xy √5xy 5xy 5xy 5y
c. 2 2
2
2
2 2 3
x
18x
18x
∛
= 3
=
3
= 3
3x 3x 32x2 33x3 3x
√ √
√
*Rewrite the fraction so the denominator is a perfect cube.
Jan 6­10:56 AM
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7­2 Day 2 Dividing Radical Expressions
January 30, 2009
Example #4: Rationalize the denominator of each expression. Assume that all variables are positive.
a.
7
5
√
b. √2x
3
√10xy
c.
∛4
∛6x
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7­2 Day 2 Dividing Radical Expressions
January 30, 2009
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 = E Em √Em √Em
=
=
=
m m2 √m2 m
√ √
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7­2 Day 2 Dividing Radical Expressions
January 30, 2009
Homework: page 377 (23 ­ 36, 37 ­ 53 odd, 56)
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