Simplify ^3√54

(1 point)

1 answer

To simplify \( \sqrt[3]{54} \), we start by factoring 54 into its prime factors:

\[ 54 = 2 \times 3^3 \]

Thus, we can rewrite \( \sqrt[3]{54} \) as:

\[ \sqrt[3]{54} = \sqrt[3]{2 \times 3^3} \]

Now we can separate the cube root of the product:

\[ \sqrt[3]{54} = \sqrt[3]{2} \times \sqrt[3]{3^3} \]

Since \( \sqrt[3]{3^3} = 3 \), we have:

\[ \sqrt[3]{54} = \sqrt[3]{2} \times 3 \]

Thus, the simplified form is:

\[ \sqrt[3]{54} = 3\sqrt[3]{2} \]

So, the final answer is:

\[ \boxed{3\sqrt[3]{2}} \]