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

Let's simplify each of the given expressions step by step by converting decimals to fractions and performing the necessary operations. --- **(a) Simplify \(0.64\)** 1. **Convert the decimal to a fraction:** \[ 0.64 = \frac{64}{100} \] 2. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD), which is 16:** \[ \frac{64 \div 16}{100 \div 16} = \frac{4}{6.25} \] However, since we need integer values, we recognize that 16 is the largest integer divisor: \[ \frac{64}{100} = \frac{16}{25} \] *(Correction: The GCD of 64 and 100 is actually 4, leading to a simplified form as follows)* \[ \frac{64 \div 4}{100 \div 4} = \frac{16}{25} \] **Final Answer:** \(\frac{16}{25}\) --- **(b) Simplify \(\sqrt[3]{0.008}\)** 1. **Convert the decimal to a fraction:** \[ 0.008 = \frac{8}{1000} \] 2. **Simplify the fraction:** \[ \frac{8}{1000} = \frac{1}{125} \] 3. **Calculate the cube root:** \[ \sqrt[3]{\frac{1}{125}} = \frac{\sqrt[3]{1}}{\sqrt[3]{125}} = \frac{1}{5} \] **Final Answer:** \(\frac{1}{5}\) --- **(c) Simplify \(\sqrt{2 \frac{7}{9}}\)** 1. **Convert the mixed number to an improper fraction:** \[ 2 \frac{7}{9} = \frac{2 \times 9 + 7}{9} = \frac{18 + 7}{9} = \frac{25}{9} \] 2. **Calculate the square root:** \[ \sqrt{\frac{25}{9}} = \frac{\sqrt{25}}{\sqrt{9}} = \frac{5}{3} \] **Final Answer:** \(\frac{5}{3}\) --- **(d) Simplify \(\frac{\sqrt{64 + 36}}{\sqrt{64} + \sqrt{36}}\)** 1. **Calculate the expressions inside the square roots:** \[ \sqrt{64 + 36} = \sqrt{100} = 10 \] \[ \sqrt{64} = 8 \quad \text{and} \quad \sqrt{36} = 6 \] 2. **Substitute the values back into the expression:** \[ \frac{10}{8 + 6} = \frac{10}{14} \] 3. **Simplify the fraction by dividing numerator and denominator by their GCD, which is 2:** \[ \frac{10 \div 2}{14 \div 2} = \frac{5}{7} \] **Final Answer:** \(\frac{5}{7}\) --- Summary of Simplified Forms: - **(a)** \(\frac{16}{25}\) - **(b)** \(\frac{1}{5}\) - **(c)** \(\frac{5}{3}\) - **(d)** \(\frac{5}{7}\)