Rounded to five decimal places, sqrt(2) + sqrt(7) = 4.05996.
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2*sqrt(12) + sqrt(27) = 2*sqrt(4*3) +sqrt(9*3) = 2*sqrt(4)*sqrt(3) + sqrt(9)*sqrt(3) = 2*2*sqrt(3) + 3*sqrt(3) = 4*sqrt(3) + 3*sqrt(3) = 7*sqrt(3)
28/sqrt(8) multiply top and bottom by sqrt(8) = 28*sqrt(8)/[sqrt(8)*sqrt(8)] = 28*sqrt(8)/8 = 7*sqrt(8)/2 But sqrt(8) = sqrt(4*2)= sqrt(4)*sqrt(2) = ±2*sqrt(2) then 7*sqrt(8)/2 = ±7*2*sqrt(2)/2 = ±7*sqrt(2)
1/[5 + 3*sqrt(2)] = [5 - 3*sqrt(2)]/{[5 + 3*sqrt(2)][5 - 3*sqrt(2)]} = [5 + 3*sqrt(2)]/[25 - 18] = [5 - 3*sqrt(2)]/7
Approximately 2.828427
There are no real root. The complex roots are: [-5 +/- sqrt(-3)] / 2