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Answer
The cube root of 64h³ is 4h.
Solution
To evaluate the cube root of 64h³, observe that 64 is a perfect cube since 64 = 4³, and the cube root of h³ is h. Therefore, we have:
√[3](64h³) = √[3](4³·h³) = 4h
Thus, the answer is 4h.
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Simplify this solution Extra Insights
To evaluate \( \sqrt[3]{64 h^{3}} \), we can break it into two separate cube roots. We know that: \[ \sqrt[3]{64 h^{3}} = \sqrt[3]{64} \cdot \sqrt[3]{h^{3}} \] Calculating each part, we find that \( \sqrt[3]{64} = 4 \) since \( 4^3 = 64 \), and \( \sqrt[3]{h^{3}} = h \) because the cube root and the cube cancel each other out. Putting it together: \[ \sqrt[3]{64 h^{3}} = 4h \] Thus, the evaluated expression is: \[ \sqrt[3]{64 h^{3}} = 4h \]
