Question

Rationalise the denominator if
$\sqrt{2} = 1.414$
Question :
$\frac{ \sqrt{2} }{2 + \sqrt{2} }$
​

Answer 1

Answer:

The answer is 0.414

Step-by-step explanation:

Given number is

      $=\dfrac{\sqrt 2}{2+\sqrt 2}$

Rationalize denominator

      $=\dfrac{\sqrt 2}{2+\sqrt 2}\times \dfrac{2-\sqrt 2}{2-\sqrt 2}\\\\=\dfrac{2\sqrt 2-(\sqrt 2)^2}{2^2-(\sqrt 2)^2}$$\boxed{\because (a+b)(a-b)=a^2-b^2}$

     $=\dfrac{2\sqrt 2-2}{4-2}\\\\=\dfrac{2(\sqrt 2-1)}{2}\\\\=\sqrt 2-1\\=1.414-1=0.414$