What is 54−−√3 simplified?

Question

Note: You will find the option to add a cubic root symbol in the Algebra (×) keyboard.

(1 point)

Answer 1

To simplify \( \sqrt[3]{54} \), we first factor 54 into its prime factors:

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

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 this into two parts:

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

Since \( \sqrt[3]{3^3} = 3 \), we can further simplify:

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

Thus, the final simplified form is:

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

Therefore, \( \sqrt[3]{54} \) simplified is \( 3 \sqrt[3]{2} \).