Chapter 8 - Section 8.1 - Solving Quadratic Equations by Completing the Square - Exercise Set - Page 484: 88

$\dfrac{1}{5}$

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}