Question 309967
{{{(sqrt(2)+5)(sqrt(2)+5)}}} Start with the given expression.



{{{sqrt(2)*sqrt(2)+5*sqrt(2)+5*sqrt(2)+5*5}}} FOIL



{{{sqrt(2*2)+5*sqrt(2)+5*sqrt(2)+5*5}}} Combine the roots using the identity {{{sqrt(x)*sqrt(y)=sqrt(x*y)}}}



{{{sqrt(4)+5*sqrt(2)+5*sqrt(2)+25}}} Multiply



{{{2+5*sqrt(2)+5*sqrt(2)+25}}} Take the square root of 4 to get 2.



{{{27+10*sqrt(2)}}} Combine like terms.



So {{{(sqrt(2)+5)(sqrt(2)+5)=27+10*sqrt(2)}}}