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Rationalizing the denominator
1.
2.
Rationalizing
3.
There is an
agreement in mathematics that we don’t leave a radical in the denominator of a fraction.
4.
So how do
we change the denominator of a fraction? (Without changing the value of the fraction, of course.)
5.
The same way
we change the denominator of any fraction! (Without changing the value of the fraction, of course.)
6.
We multiply the
denominator by the same number. and the numerator
7.
By what number
to a rational number? to change it can we multiply
8.
The answer is
. . . . . . by itself!
9.
Remember, is the
number we square to get n . we’d better get n . So when we square it,
10.
In our fraction,
to get the radical out of the denominator, we can multiply numerator and denominator by .
11.
In our fraction,
to get the radical out of the denominator, we can multiply numerator and denominator by .
12.
Because we are
changing the denominator we call this process rationalizing . to a rational number,
13.
Rationalize the denominator:
(Don’t forget to simplify)
14.
Rationalize the denominator:
(Don’t forget to simplify) (Don’t forget to simplify)
15.
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.
16.
Multiply by the
conjugate. FOIL numerator and denominator. Next Simplify:
17.
Simplify ·
=
18.
Combine like terms
Try this on your own:
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