#### 6(47/11)^(3/2)

February 22, 2026

#### 6(47/11)^(3/2)

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Volume: \(x \cdot 2x \cdot 3x = 6x^3 = 6 \left(\sqrt{\frac{47}{11}}\right)^3\).
Calculate: \(x^3 = \left(\frac{47}{11}\right)^{3/2}\), \(6 \times \left(\frac{47}{11}\right)^{3/2}\).
Approximate \(x \approx 2.02\), \(x^3 \approx 8.20\), volume \(\approx 6 \times 8.20 = 49.2\).
A ladder leans against a wall, reaching a height of 12 meters. If the base is 5 meters from the wall, what is the length of the ladder?
Use Pythagoras: \(c^2 = 12^2 + 5^2 = 144 + 25 = 169\).
\(c = \sqrt{169} = 13\) meters.

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