Jse logarithm table to evaluate: \( \frac{15.36^{2} \times \sqrt[3]{0.7342}}{173.6} \) correct to \( 3 s . f \).
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Bonus Knowledge
To evaluate \( \frac{15.36^{2} \times \sqrt[3]{0.7342}}{173.6} \) correctly to three significant figures, we can make use of logarithms to simplify the calculation. First, compute \( 15.36^2 \): \[ 15.36^2 = 235.9296 \] Next, we need to find \( \sqrt[3]{0.7342} \). Using logarithms, this can be approached as follows: \[ \sqrt[3]{0.7342} = 0.7342^{1/3} \] Using a scientific calculator or logarithm table, we get: \[ \sqrt[3]{0.7342} \approx 0.9034 \] Now we combine these values: \[ 15.36^2 \times \sqrt[3]{0.7342} \approx 235.9296 \times 0.9034 \approx 213.369 \] Now divide by \( 173.6 \): \[ \frac{213.369}{173.6} \approx 1.228 \] Finally, rounding \( 1.228 \) to three significant figures gives us: \[ \boxed{1.23} \]
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