How do you expand ln sqrt(a(b^2+c^2))?

$= \ln {\left(a \left({b}^{2} + {c}^{2}\right)\right)}^{\frac{1}{2}}$
$= \frac{1}{2} \ln \left(a \left({b}^{2} + {c}^{2}\right)\right)$
$= \frac{1}{2} \ln a + \frac{1}{2} \ln \left({b}^{2} + {c}^{2}\right)$