1.) (2+√3)/(5+√7)

2.) (2x+√5x)/(5+√x)

3.) (2+√15)/(3+4√30m)

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- Aug 7th 2008, 03:11 PMep78Rationalize-help
1.) (2+√3)/(5+√7)

2.) (2x+√5x)/(5+√x)

3.) (2+√15)/(3+4√30m) - Aug 7th 2008, 04:37 PMo_O
Take the conjugate of the denominator. For the #1, the conjugate of $\displaystyle 5 + \sqrt{7}$ is: $\displaystyle 5 {\color{red}-} \sqrt{7}$.

Take the conjugate and multiply it to both the numerator and denominator:

$\displaystyle \frac{2 + \sqrt{3}}{5 + \sqrt{7}} \cdot \frac{5 {\color{red}-} \sqrt{7}}{5 {\color{red}-} \sqrt{7}} \: \: = \: \: \frac{10 -2\sqrt{7} +5\sqrt{3} - \sqrt{21}}{25 - 7} \: \: = \: \: \ldots$

The other questions use exactly the same method. Post if you have any more problems! - Aug 7th 2008, 05:50 PMep78
- Aug 7th 2008, 05:52 PMep78
- Aug 7th 2008, 05:52 PMo_O
Yes you would further simplify it. Not much to do though.