Answer
$\dfrac{1+i\sqrt{2}}{2}$
Work Step by Step
Using $i=\sqrt{-1}$ and the properties of radicals, the given expression, $ \dfrac{7+\sqrt{-98}}{14} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{7+\sqrt{-1}\cdot\sqrt{98}}{14}
\\\\= \dfrac{7+i\cdot\sqrt{49\cdot2}}{14}
\\\\= \dfrac{7+i\cdot\sqrt{(7)^2\cdot2}}{14}
\\\\= \dfrac{7+i\cdot7\sqrt{2}}{14}
\\\\=
\dfrac{7+7i\sqrt{2}}{14}
\\\\=
\dfrac{7(1+i\sqrt{2})}{14}
\\\\=
\dfrac{\cancel{7}(1+i\sqrt{2})}{\cancel{7}\cdot2}
\\\\=
\dfrac{1+i\sqrt{2}}{2}
.\end{array}