Without using a calculator and by converting decimals into fractions, simplify the following: \( \begin{array}{ll}\text { (a) } \\ \begin{array}{ll}0,64 & \text { (b) } \sqrt[3]{0,008} \\ \text { (c) } \sqrt{2 \frac{7}{9}} & \text { (d) } \frac{\sqrt{64+36}}{\sqrt{64}+\sqrt{36}}\end{array}\end{array}> \)

To simplify the given mathematical expressions, we will convert decimals into fractions and work through the operations. (a) \(0.64\) can be expressed as the fraction \(\frac{64}{100}\). Simplifying this, we get: \[ \frac{64 \div 4}{100 \div 4} = \frac{16}{25}. \] (b) \(\sqrt[3]{0.008}\) can be simplified by rewriting \(0.008\) as \(\frac{8}{1000}\) or \(\frac{8}{10^3}\). Therefore, we have: \[ \sqrt[3]{0.008} = \sqrt[3]{\frac{8}{1000}} = \frac{\sqrt[3]{8}}{\sqrt[3]{1000}} = \frac{2}{10} = \frac{1}{5}. \] (c) To simplify \(\sqrt{2 \frac{7}{9}}\), we first convert the mixed number into an improper fraction: \[ 2 \frac{7}{9} = \frac{18}{9} + \frac{7}{9} = \frac{25}{9}. \] Now, taking the square root: \[ \sqrt{2 \frac{7}{9}} = \sqrt{\frac{25}{9}} = \frac{\sqrt{25}}{\sqrt{9}} = \frac{5}{3}. \] (d) For \(\frac{\sqrt{64+36}}{\sqrt{64}+\sqrt{36}}\), we first compute \(64 + 36 = 100\), leading to: \[ \frac{\sqrt{100}}{\sqrt{64}+\sqrt{36}} = \frac{10}{8 + 6} = \frac{10}{14}. \] Simplifying this fraction: \[ \frac{10 \div 2}{14 \div 2} = \frac{5}{7}. \] In summary: (a) \(\frac{16}{25}\) (b) \(\frac{1}{5}\) (c) \(\frac{5}{3}\) (d) \(\frac{5}{7}\)