\( \begin{array}{ll}\text { 4.2. } & 2(\sqrt[3]{64}+\sqrt{25})=18 \\ \text { 4.8. } & \left(3,6 \times 10^{6}\right)-\left(5,2 \times 10^{5}\right) \\ \text { 4.4. } & \frac{1}{2}+2 \frac{3}{4}-\frac{3}{8}\end{array} \)
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The Deep Dive
Let's break down the problems in a fun way! First up, the expression \( 2(\sqrt[3]{64}+\sqrt{25}) \). Calculating the cube root of 64 gives you 4 (since \(4^3 = 64\)), and the square root of 25 is 5. So we have \( 2(4 + 5) = 2(9) = 18 \). Ta-da! You can see why the equation holds true! Next, for the second problem \( (3.6 \times 10^{6}) - (5.2 \times 10^{5}) \), align the numbers by powers of 10. Here’s a fun tip: convert \( 5.2 \times 10^{5} \) to the same power as \( 3.6 \times 10^{6} \) by rewriting it as \( 0.52 \times 10^{6} \). Then, \( 3.6 - 0.52 = 3.08 \), giving you \( 3.08 \times 10^{6} \)! Lastly, for that last number crunching adventure! The numbers \( \frac{1}{2} + 2\frac{3}{4} - \frac{3}{8} \) can be tricky if you're not careful. Convert everything to eighths: \( \frac{1}{2} = \frac{4}{8} \), \( 2\frac{3}{4} = \frac{6}{4} = \frac{12}{8} \). Now you have \( \frac{4}{8} + \frac{12}{8} - \frac{3}{8} = \frac{13}{8} \) or \( 1\frac{5}{8} \)!