Transcript 6 2 There is an agreement in mathematics that we don’t leave a radical in the denominator of a fraction. 3

3
6
6
2
There is an agreement
in mathematics
that we don’t leave a radical
in the denominator
of a fraction.
1
3
So how do we change the
denominator of a fraction?
(Without changing the value of
the fraction, of course.)
1
3
The same way we change the
denominator of any fraction!
(Without changing the value of
the fraction, of course.)
1 1 3 3


4 4  3 12
We multiply the denominator
and the numerator
by the same number.
1 1 3 3


4 4  3 12
By what number
can we multiply
3
to change it
to a rational number?
1
3
The answer is . . .
. . . by itself!
3  3
1
3
2
3  3
Remember,

2
n  n
is the number we square
to get n.
So when we square it,
we’d better get n.
In our fraction, to get the radical
out of the denominator,
we can multiply numerator and
denominator by 3.
1
3
In our fraction, to get the radical
out of the denominator,
we can multiply numerator and
denominator by 3.
1
1 3
3


3
3 3
3
Because we are changing
the denominator
to a rational number,
we call this process
rationalizing.
3
1

3 3
Rationalize the denominator:
2
4 2 4 2
4

2 2

2 2
2
2
Rationalize the denominator:
8
8 12
96



12
12 12 12
6
4 6

3
12
3
When there is a binomial with a
radical in the denominator of a
fraction, you find the conjugate and
multiply. This gives a rational
denominator.
Ex:
5  6  Conjugat e: 5  6
3  2 2  Conjugat e: 3  2 2
What is conjugate of2 7  3?
Answer: 2 7  3
Simplify:
56
53
56
56 53


53
53 53
5  3 5  6 5  18
59
Next
Multiply by
the conjugate.
FOIL numerator
and denominator.
2
Simplify 5 + 2
5– 2
2
·
5 2 5– 2
2(5) – 2 2
2
2
5 – ( 2)
10  2 2
25 – 2
=
10 – 2 2
23
23  9 5
4
Combine like terms
Try this on your own:
6
3 2
3 62 3
Answer :
7
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