Answer
$\dfrac{7x\sqrt[]{7}}{10}$
Work Step by Step
Using the properties of radicals, then,
\begin{array}{l}
\dfrac{3x\sqrt[]{7}}{5}+\sqrt[]{\dfrac{7x^2}{100}}
\\\\=
\dfrac{3x\sqrt[]{7}}{5}+\dfrac{x\sqrt{7}}{10}
\\\\=
\dfrac{2(3x\sqrt[]{7})+x\sqrt{7}}{10}
\\\\=
\dfrac{6x\sqrt[]{7}+x\sqrt{7}}{10}
\\\\=
\dfrac{7x\sqrt[]{7}}{10}
.\end{array}