Question 714958
There's probably some trick to solving or simplifying nested radicals, but it's not coming to mind at the moment.


Anyways, there's a much simpler way to see why the answers are {{{sqrt(2)}}} and {{{sqrt(5)}}}


Rewrite the last term {{{sqrt(10)}}} as 


{{{sqrt(10)=sqrt(2*5)}}}


{{{sqrt(10)=sqrt(2)*sqrt(5)}}}


Now use the idea that if the roots of {{{x^2 - bx+c}}} are {{{p}}} and {{{q}}}, then {{{b = p+q}}} and {{{c = p*q}}}


So if you replace p with {{{sqrt(2)}}} and q with {{{sqrt(5)}}}, you get 


{{{b = sqrt(2)+sqrt(5)}}} and {{{q = sqrt(2)*sqrt(5)}}}



Hopefully that makes sense to you.