What is 54−−√3

Question

simplified?

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

Answer 1

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

\[ 54 = 2 \times 27 = 2 \times 3^3 \]

Now we can take the cube root:

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

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:

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

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

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