Rationalize-help

**ep78** · August 7th 2008, 03:11 PM

1.) (2+√3)/(5+√7)

2.) (2x+√5x)/(5+√x)

3.) (2+√15)/(3+4√30m)

**o_O** · August 7th 2008, 04:37 PM

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!

**ep78** · August 7th 2008, 05:50 PM

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?

**ep78** · August 7th 2008, 05:52 PM

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?

**o_O** · August 7th 2008, 05:52 PM

Yes you would further simplify it. Not much to do though.

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