Rationalizing the Denominator
Rationalize the denominator:
Solution
To eliminate the square root, we can multiply by the conjugate
of
![](./articles_imgs/937/ration82.gif)
We multiply
by 1 written in
the form
|
![](./articles_imgs/937/ration84.gif) |
Multiply the numerators and multiply
the denominators. |
![](./articles_imgs/937/ration85.gif) |
In the numerator, use the Distributive
Property. |
![](./articles_imgs/937/ration86.gif) |
In the denominator, use the FOIL method. |
![](./articles_imgs/937/ration87.gif) |
In the denominator, combine like terms.
|
![](./articles_imgs/937/ration88.gif) |
We normally do not leave a negative
number in the denominator. Therefore,
multiply by 1 in the form
|
![](./articles_imgs/937/ration90.gif) |
Multiply the numerators and multiply
the denominators. |
![](./articles_imgs/937/ration91.gif) |
|