Answer
$\dfrac{1}{5}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{9}{10}-\sqrt[]{\dfrac{49}{100}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{9}{10}-\sqrt[]{\left( \dfrac{7}{10} \right)^2}
\\\\=
\dfrac{9}{10}-\dfrac{7}{10}
\\\\=
\dfrac{9-7}{10}
\\\\=
\dfrac{2}{10}
\\\\=
\dfrac{\cancel{2}}{\cancel{2}\cdot5}
\\\\=
\dfrac{1}{5}
.\end{array}