Rationalize-help

• Aug 7th 2008, 04:11 PM
ep78
Rationalize-help
1.) (2+√3)/(5+√7)

2.) (2x+√5x)/(5+√x)

3.) (2+√15)/(3+4√30m)
• Aug 7th 2008, 05:37 PM
o_O
Take the conjugate of the denominator. For the #1, the conjugate of $5 + \sqrt{7}$ is: $5 {\color{red}-} \sqrt{7}$.

Take the conjugate and multiply it to both the numerator and denominator:
$\frac{2 + \sqrt{3}}{5 + \sqrt{7}} \cdot \frac{5 {\color{red}-} \sqrt{7}}{5 {\color{red}-} \sqrt{7}} \: \: = \: \: \frac{10 -2\sqrt{7} +5\sqrt{3} - \sqrt{21}}{25 - 7} \: \: = \: \: \ldots$

The other questions use exactly the same method. Post if you have any more problems!
• Aug 7th 2008, 06:50 PM
ep78
Quote:

Originally Posted by o_O
Take the conjugate of the denominator. For the #1, the conjugate of $5 + \sqrt{7}$ is: $5 {\color{red}-} \sqrt{7}$.

Take the conjugate and multiply it to both the numerator and denominator:
$\frac{2 + \sqrt{3}}{5 + \sqrt{7}} \cdot \frac{5 {\color{red}-} \sqrt{7}}{5 {\color{red}-} \sqrt{7}} \: \: = \: \: \frac{10 -2\sqrt{7} +5\sqrt{3} - \sqrt{21}}{25 - 7} \: \: = \: \: \ldots$

The other questions use exactly the same method. Post if you have any more problems!

So is that the final answer or would you have to simplyfy it?
• Aug 7th 2008, 06:52 PM
ep78
Quote:

Originally Posted by ep78
So is that the final answer or would you have to simplyfy it?

sorry..nevermind..but would you have to split the √21? or just leave the numerator as it is?
• Aug 7th 2008, 06:52 PM
o_O
Yes you would further simplify it. Not much to do though.