Question 99152
It is the special case of rectangle where all sides have same length, which we denote a. There is formula for surface area of rectangle with side a {{{S = a^2}}} Thus {{{S = (sqrt(3)+sqrt(5))^2}}}
we can use {{{(a+b)^2=a^2+2ab+b^2}}}
3+2*(sqrt(3)*sqrt(5)+5
now we can use {{{sqrt(x) = x^(1/2)}}} and {{{a^x*b^x=(a*b)^x}}} and we get
={{{8+(3*5)^1/2}}}
={{{8+15^1/2}}}
={{{8+sqrt(15)}}} which is around 11.873

If you are interested in higher mathematics, area of rectangle can also be computed using definite integral {{{int(a,dx,a,b)}}} where a is constant function and integration bounds define left and right side, in our case it would be {{{int(sqrt(3)+sqrt(5),dx,0,sqrt(3)+sqrt(5))}}} = F(b)-F(a) ={{{(sqrt(3)+sqrt(5))*(sqrt(3)+sqrt(5))-0}}} whic leads to same result.