[tex]~~~\dfrac{1+ \sqrt 2}{\sqrt 2 -1}\\\\\\=\dfrac{\left(1+ \sqrt 2\right)\left(\sqrt 2 +1 \right)}{ \left(\sqrt 2 - 1 \right)\left( \sqrt 2 +1\right)}\\\\\\=\dfrac{\sqrt 2 +1 + \left(\sqrt 2 \right)^2 + \sqrt 2}{\left(\sqrt 2 \right)^2 -1 }\\\\\\=\dfrac{2\sqrt 2 +1 + 2}{2-1}\\\\\\=\dfrac{3+2\sqrt 2}{1}\\\\\\=3+2\sqrt 2\\\\\\=3+2(1.141)\\\\\\=5.828[/tex]
