# Question efd90

Sep 6, 2016

$- .4407$ nearly..According to the practice (convention ) that sqrt# ( positive number) is the positive square root, it is OK, See explanation,

#### Explanation:

Under strict mathematical norms, $\sqrt{2} = {2}^{\frac{1}{2}} = \pm 1.414213562 , ,$.

Here, only the convention of choosing the positive square root makes the function real.

So,

$\ln \left(\sqrt{\sqrt{2} - 1}\right)$

$= \ln \left(\sqrt{1.414213562 \ldots - 1}\right)$

$= \ln \left(\sqrt{0.412313562} \ldots\right)$

$= \ln \left(0.643594252\right)$

$= - .440686793 \ldots$, nearly..