1. ## Rationalize-help

1.) (2+√3)/(5+√7)

2.) (2x+√5x)/(5+√x)

3.) (2+√15)/(3+4√30m)

2. 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!

3. 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?

4. 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?

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