Rationalize the denominator of (sqrt(5)+sqrt(2))/(sqrt(5)-sqrt(2)). The answer can be written as (A+Bsqrt(C))/D, where A, B, C, and D are integers. D is positive and C is not divisible by the square of any prime. If the greatest common divisor of A, B, and D is 1, find A+B+C+D.

Guest Jun 15, 2019

#1**+6 **

\(\frac{\sqrt5+\sqrt2}{\sqrt5-\sqrt2}\)

the bottom is sqrt5 **-** sqrt 2

You just have to multiply both the top and the bottom by sqrt5 **+ **sqrt2

That fact that the top is the same is just a coincidence.

Melody Jun 15, 2019

#6**+2 **

Why did you vote my answer down Hectictar?

Do you think people should be spoon fed all their answers?

Is a good hint worse than no answer at all?

I am not cross, I am just disillusioned with the site in general.

Melody Jun 16, 2019

#8**+3 **

I'm sorry Melody. I did give your answer a point but then took it back off a few seconds later. To be honest, I can't give you a good reason why I did that. I don't really remember what I was thinking, but maybe it was to make yours and CPhill's answer have equal number of points. I don't think that I had a good reason.

hectictar
Jun 16, 2019