Question

cubed √54 simplified

Answer 1

To simplify the expression \( \sqrt[3]{54} \), we can factor 54 into its prime factors.

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

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

Using the property of cube roots, we can separate the factors:
\[
\sqrt[3]{54} = \sqrt[3]{2} \times \sqrt[3]{3^3}
\]

Since \( \sqrt[3]{3^3} = 3 \), we have:
\[
\sqrt[3]{54} = \sqrt[3]{2} \times 3
\]

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

So, \( \sqrt[3]{54} = 3 \sqrt[3]{2} \).