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Answer 1 · 2016-09-06T02:54:53

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

Under strict mathematical norms, $sqrt 2=2^(1/2)=+-1.414213562,,$ .

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

So,

$ln(sqrt(sqrt2-1))$

$=ln(sqrt(1.414213562...-1))$

$=ln(sqrt0.412313562...)$

$=ln(0.643594252)$

$=-.440686793...$ , nearly..