Question

Simplify cube root
3√54

Answer 1

To simplify the cube root of 54, we first need to factor 54 into its prime factors:

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

Now, we can express the cube root:

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

We can break this down using the property of cube roots:

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

Since the cube root of \(3^3\) is 3:

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

So, we can express this as:

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

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

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