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

Let's simplify each expression step by step. (a) To simplify \( \sqrt{0.64} \), we convert \( 0.64 \) into a fraction: \[ 0.64 = \frac{64}{100} = \frac{16}{25} \] Now, taking the square root gives: \[ \sqrt{0.64} = \sqrt{\frac{16}{25}} = \frac{\sqrt{16}}{\sqrt{25}} = \frac{4}{5} \] (b) For \( \sqrt[3]{0.008} \), we also convert it to a fraction: \[ 0.008 = \frac{8}{1000} = \frac{1}{125} \] Now taking the cube root yields: \[ \sqrt[3]{0.008} = \sqrt[3]{\frac{1}{125}} = \frac{\sqrt[3]{1}}{\sqrt[3]{125}} = \frac{1}{5} \] (c) To simplify \( \sqrt{2 \frac{7}{9}} \), first, convert the mixed number to an improper fraction: \[ 2 \frac{7}{9} = \frac{18}{9} + \frac{7}{9} = \frac{25}{9} \] Taking the square root gives: \[ \sqrt{2 \frac{7}{9}} = \sqrt{\frac{25}{9}} = \frac{\sqrt{25}}{\sqrt{9}} = \frac{5}{3} \] (d) For \( \frac{\sqrt{64+36}}{\sqrt{64}+\sqrt{36}} \), let's simplify: First, calculate the square roots: \[ \sqrt{64} = 8 \text{ and } \sqrt{36} = 6 \] Now, the numerator becomes: \[ \sqrt{64+36} = \sqrt{100} = 10 \] Thus, we have: \[ \frac{\sqrt{64+36}}{\sqrt{64}+\sqrt{36}} = \frac{10}{8+6} = \frac{10}{14} = \frac{5}{7} \] In summary: (a) \( \frac{4}{5} \), (b) \( \frac{1}{5} \), (c) \( \frac{5}{3} \), (d) \( \frac{5}{7} \).