Question

Express 1+√2/√2-1 with rational denominator and find its value given√2= 1.414

pleasee solve it guys T_T​

Answer 1

`~~~(1+ \sqrt 2)/(\sqrt 2 -1)\\\\\\=(\left(1+ \sqrt 2\right)\left(\sqrt 2 +1 \right))/( \left(\sqrt 2 - 1 \right)\left( \sqrt 2 +1\right))\\\\\\=(\sqrt 2 +1 + \left(\sqrt 2 \right)^2 + \sqrt 2)/(\left(\sqrt 2 \right)^2 -1 )\\\\\\=(2\sqrt 2 +1 + 2)/(2-1)\\\\\\=(3+2\sqrt 2)/(1)\\\\\\=3+2\sqrt 2\\\\\\=3+2(1.141)\\\\\\=5.828`