Simplify 3√54

Question

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Answer 1

To simplify \( 3\sqrt[3]{54} \), we start by breaking down the number inside the cubic root.

First, we factor \( 54 \): \[ 54 = 2 \times 27 = 2 \times 3^3 \]

Now we can rewrite \( 3\sqrt[3]{54} \): \[ 3\sqrt[3]{54} = 3\sqrt[3]{2 \times 3^3} \]

Using the property of cubic roots, we can separate the factors: \[ 3\sqrt[3]{54} = 3\left(\sqrt[3]{2} \times \sqrt[3]{3^3}\right) \]

Since \( \sqrt[3]{3^3} = 3 \), we can substitute that in: \[ 3\sqrt[3]{54} = 3\left(\sqrt[3]{2} \times 3\right) \] \[ = 3^2 \sqrt[3]{2} = 9\sqrt[3]{2} \]

Thus, the simplified form of \( 3\sqrt[3]{54} \) is: \[ \boxed{9\sqrt[3]{2}} \]