Aim: How do we rationalize a denominator containing a radical? Do Now: 1. Circle all the irrational...
7
Aim: How do we rationalize a denominator containing a radical? ow: 1. Circle all the irrational numbers: 20 , 30 , 16 , 8 , 7 , 5 , 4 , 3 , 2 2. Simplify: 4 1 3. Simplify: 5 1 HW: Worksheet
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Transcript of Aim: How do we rationalize a denominator containing a radical? Do Now: 1. Circle all the irrational...
Aim: How do we rationalize a denominator containing a radical?
Do Now: 1. Circle all the irrational numbers:
20,30,16,8,7,5,4,3,2
2. Simplify:4
1
3. Simplify:5
1
HW: Worksheet
4
14
5
1
We can only simplify since is rational number.
? What happen to
5
1
5
We cannot simplify by using regular method
since the denominator is an irrational number.
Therefore, we need to do something to make the denominator become a rational number.
This procedure is called rationalize the denominator (where the denominator is not a rational number) means to find an equivalent fraction in which the denominator is a rational number.
How do we rationalize the irrational denominator?
1. Multiply the irrational denominator by the exact same irrational number to get square and then get rid of the square root
2. Multiply the numerator by the number as the denominator did
3. Simplify the resulting fraction
55
51
5
5
25
5
Rationalize:33
9
1. Multiply the denominator by its conjugate which is
33
2. Multiply the numerator by the same number as the denominator did
3. Simplify the resulting fraction
)33)(33(
9
)33)(33(
)33(9
239
3927
6
3927
2
339
The reason why we multiply the denominator by its conjugate is to get the difference of two squares, therefore we can get rid of the radical.
To rationalize the radical denominator, we need to multiply the denominator by its conjugate
22))(( yxyxyx
11
9
Rationalize:1111
119
211
119
11
119
Rationalize:. 25
23
)25)(25(
)25)(23(
22
2
25
2252315
225
22815
23
2817
202
40
Rationalize the denominator
1.
33
18
2.
12
42
3.
52
)33(3
256
