Question

Find the value of root 2 by 2+root 2 to three places of decimal, if it is given that root 2= 1.414

Answer 1

Heya there,
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 :

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

Hope this helps!!!

If you have any doubt regarding to my answer, feel free to ask in the comment section or inbox me if needed.

@Mahak24

Thanks...
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