1 + 83 − 2\;\frac{1\;+\;\sqrt{8}}{3\;-\;\sqrt{2}}3−21+8
Rationalizing by multiplying through with 3+23 + \sqrt{2}3+2,
( 1 + 83 − 2)( 3 + 23 + 2)= 3 + 2 + 38 + 49 − 2\left( \frac{\;1\;+\;\sqrt{8}}{3\;-\;\sqrt{2}} \right) \left( \frac{\;3\;+\;\sqrt{2}}{3\;+\;\sqrt{2}} \right) = \frac{\;3\;+\;\sqrt{2}\;+\;3\sqrt{8}\;+\;4}{9\;-\;2}(3−21+8)(3+23+2)=9−23+2+38+4
= 3 + 2 + 34 × 2 + 47\frac{\;3\;+\;\sqrt{2}\;+\;3\sqrt{4\;\times\;2}\;+\;4}{7}73+2+34×2+4
= 7 + 727=1+2\frac{\;7\;+\;7\sqrt{2}}{7} = 1 + \sqrt{2}77+72=1+2
