1. ## simple surd thing

explain why 1/((sqrt3)-1) = 1/((sqrt3)-1) x ((sqrt3) +1)/((sqrt3) +1)
i think the obvious answer is that ((sqrt3) +1)/((sqrt3) +1) = 1 but i dont know if thats the answer im supposed to be looking for...

2. Originally Posted by furor celtica
explain why 1/((sqrt3)-1) = 1/((sqrt3)-1) x ((sqrt3) +1)/((sqrt3) +1)
i think the obvious answer is that ((sqrt3) +1)/((sqrt3) +1) = 1 but i dont know if thats the answer im supposed to be looking for...
That's exactly the reason. If you multiply a number by 1, you get what you started with.

And from here, you can rationalise the denominator.

3. Either that or:

$\frac{1}{\sqrt{3}+1}\times \frac{\sqrt{3}+1}{\sqrt{3}+1}$

$=\frac{(\sqrt{3}+1)}{(\sqrt{3}+1)(\sqrt{3}+1)}$

$=\frac{1}{\sqrt{3}+1}$

4. hahaha the whole time i was thinking 'damn i need to find something more complicated'
thanks guys