MCV 4U ­ 1.1 (Rationalizing)
February 08, 2017
What's Going On?
True or False?
Rationalizing
A Tricky One
Learning Goal ­ I will be able to rationalize a denominator
by multiplying by the conjugate .
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MCV 4U ­ 1.1 (Rationalizing)
February 08, 2017
True or False?
For each statement
i. determine if it is true or false.
ii. if it is false, give a counter example, if it is true provide 2 examples.
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MCV 4U ­ 1.1 (Rationalizing)
February 08, 2017
True or False?
3
MCV 4U ­ 1.1 (Rationalizing)
February 08, 2017
Rationalizing
The process of changing a denominator from a radical to a rational number is called rationalizing the denominator. Later in the course, we will need to use these techniques to rationalize the numerator.
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MCV 4U ­ 1.1 (Rationalizing)
February 08, 2017
Rationalizing
One Term Radical in the Denominator
When the denominator is a one‐term radical, we multiply both the numerator and the denominator by the denominator.
5
MCV 4U ­ 1.1 (Rationalizing)
February 08, 2017
Rationalizing
One Term Radical in the Denominator
When the denominator is a one‐term radical, we multiply both the numerator and the denominator by the denominator.
6
MCV 4U ­ 1.1 (Rationalizing)
February 08, 2017
Rationalizing
One Term Radical in the Denominator
When the denominator is a one‐term radical, we multiply both the numerator and the denominator by the denominator.
7
MCV 4U ­ 1.1 (Rationalizing)
February 08, 2017
Rationalizing
Expand and Simplify
(a + b)2
(a + b)(a ­ b)
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MCV 4U ­ 1.1 (Rationalizing)
February 08, 2017
Rationalizing
Two Term Radical in the Denominator
When the denominator is a two‐term radical, we multiply the numerator and the denominator by the conjugate.
9
MCV 4U ­ 1.1 (Rationalizing)
February 08, 2017
Rationalizing
Two Term Radical in the Denominator
When the denominator is a two‐term radical, we multiply the numerator and the denominator by the conjugate.
10
MCV 4U ­ 1.1 (Rationalizing)
February 08, 2017
11
MCV 4U ­ 1.1 (Rationalizing)
February 08, 2017
Rationalizing
Two Term Radical in the Denominator
When the denominator is a two‐term radical, we multiply the numerator and the denominator by the conjugate.
12
MCV 4U ­ 1.1 (Rationalizing)
February 08, 2017
A Tricky One
13
MCV 4U ­ 1.1 (Rationalizing)
February 08, 2017
14
MCV 4U ­ 1.1 (Rationalizing)
February 08, 2017
15