Answer
$\sqrt{5}$
Work Step by Step
Using the properties of radicals, then,
\begin{array}{l}
\dfrac{\sqrt{45}}{10}+\dfrac{7\sqrt{5}}{10}
\\\\=
\dfrac{\sqrt{9\cdot5}}{10}+\dfrac{7\sqrt{5}}{10}
\\\\=
\dfrac{3\sqrt{5}}{10}+\dfrac{7\sqrt{5}}{10}
\\\\=
\dfrac{10\sqrt{5}}{10}
\\\\=
\sqrt{5}
.\end{array}