SOLUTION: I need help simplifying this expression: {{{sqrt(24+8sqrt(5))}}} I removed the common factor out of the square root to obtain {{{2sqrt(6+2sqrt(5))}}}, but the answer key says it

Algebra ->  Radicals -> SOLUTION: I need help simplifying this expression: {{{sqrt(24+8sqrt(5))}}} I removed the common factor out of the square root to obtain {{{2sqrt(6+2sqrt(5))}}}, but the answer key says it       Log On


   



Question 1030250: I need help simplifying this expression:
sqrt%2824%2B8sqrt%285%29%29
I removed the common factor out of the square root to obtain 2sqrt%286%2B2sqrt%285%29%29, but the answer key says it is 2%2B2sqrt%285%29.
How is it possible? Am I missing out on a rule here?

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2824%2B8sqrt%285%29%29
sqrt%284%2B8sqrt%285%29%2B20%29

sqrt%284%2B8sqrt%285%29%2B%282sqrt%285%29%29%5E2%29
%28a%2Bb%29%5E2+=+a%5E2%2B2ab%2Bb%5E2 using this identity
we get
sqrt%28%282%2B2sqrt%285%29%29%5E2%29

2%2B2sqrt%285%29