# Math Help - how does this work?

1. ## how does this work?

I know that

1+√5 = 3√(2+√5) = 1.618033989
2

but what is the math behind it specifically a way to simplify
3√(2+√5) to 1+√5

2

Thanks

2. Just to make this clear its (1+√5)/2 which equals 3√(2+√5) I hope that is clear.

3. Hello,
Originally Posted by Smoriginal
Just to make this clear its (1+√5)/2 which equals 3√(2+√5) I hope that is clear.
$\frac{1+\sqrt{5}}{2}=\sqrt[3]{2+\sqrt{5}}$

You can prove it by cubing both sides. This is all I can see for the moment...

(note : $(a+b)^3=a^3+b^3+3ab^2+3a^2b$)