Question

simplify cubit root ^3 radical 54

Answer 1

To simplify the cube root of 54, we can start by factoring 54 into its prime factors:

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

Now, we can express \(\sqrt[3]{54}\) using its prime factors:

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

Using properties 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:

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

Thus, the simplified form of the cube root of 54 is:

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