# how does this work?

• September 16th 2008, 07:30 AM
Smoriginal
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

2

Thanks

• September 16th 2008, 07:35 AM
Smoriginal
Just to make this clear its (1+√5)/2 which equals 3√(2+√5) I hope that is clear.
• September 16th 2008, 08:02 AM
Moo
Hello,
Quote:

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