Question 1016336
{{{(sqrt(a) + sqrt(b))^2 = a+2sqrt(ab) +b}}}

If we let {{{10 + sqrt(84) = a+2sqrt(ab) +b}}} we then get

a + b = 10 and ab = 21 by equating coefficients of like terms.

==> {{{b = 21/a}}}, and so {{{a+21/a = 10}}}, or {{{a^2-10a+21=0}}}

==> a = 3 or 7, which gives b = 7 or 3, respectively.

Either way, we get {{{sqrt(10+sqrt(84)) = sqrt(3) +sqrt(7)}}}.