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Simplify. \( \sqrt[3]{81}+2 \sqrt[3]{3} \)

Ask by Stewart Barber. in the United States
Feb 22,2025

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\( 5\sqrt[3]{3} \)

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To simplify \( \sqrt[3]{81} + 2 \sqrt[3]{3} \), we start by breaking down \( 81 \): \[ 81 = 3^4 \] Thus, we can rewrite \( \sqrt[3]{81} \) as: \[ \sqrt[3]{81} = \sqrt[3]{3^4} = 3^{4/3} = 3^{1 + 1/3} = 3 \cdot 3^{1/3} = 3\sqrt[3]{3} \] Now substituting this back in, we have: \[ \sqrt[3]{81} + 2\sqrt[3]{3} = 3\sqrt[3]{3} + 2\sqrt[3]{3} \] Now we can factor out \( \sqrt[3]{3} \): \[ (3 + 2)\sqrt[3]{3} = 5\sqrt[3]{3} \] So, the simplified form is: \[ \boxed{5\sqrt[3]{3}} \]

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