Question

find root 2 upon 2 + root 2 is root 2 is equal to 1.414

Answer 1

Here is the answer you were looking for:

\frac{ \sqrt{2} }{2  + \sqrt{2} }  \\  

On rationalizing the denominator we get,

=  \frac{ \sqrt{2} }{2 +  \sqrt{2} } \times  \frac{2 -  \sqrt{2} }{2 -  \sqrt{2} }   \\  

Using the identity :  

=  \frac{ \sqrt{2}(2 -  \sqrt{2} ) }{ {(2)}^{2} -  {( \sqrt{2} )}^{2}  }  \\  \\  =  \frac{2 \sqrt{2}  - 2}{4 - 2}  \\  \\  =  \frac{2 \sqrt{2}  - 2}{2}  \\  \\  =  \frac{2( \sqrt{2} - 1) }{2}  \\  \\  =  \sqrt{2}  - 1 \\  \\  = 1.414 - 1 \\  \\  = 0.414