Question

simplify
3\sqrt3{81}
\bigcirc\\ 12\sqrt3{3}
\bigcirc\\ 6\sqrt3{3}
\bigcirc\\ 3\sqrt3{3}
\bigcirc\\ 9\sqrt3{3}

Explanation:

Step1: Factor 81

We know that \(81 = 27\times3\), and \(27 = 3^3\). So, \(\sqrt[3]{81}=\sqrt[3]{3^3\times3}\).

Step2: Simplify the cube root

Using the property of cube roots \(\sqrt[3]{ab}=\sqrt[3]{a}\times\sqrt[3]{b}\) (where \(a = 3^3\) and \(b = 3\)), we get \(\sqrt[3]{3^3\times3}=\sqrt[3]{3^3}\times\sqrt[3]{3}\). Since \(\sqrt[3]{3^3}=3\), then \(\sqrt[3]{81}=3\sqrt[3]{3}\).

Step3: Multiply by the coefficient

Now, we have \(3\sqrt[3]{81}=3\times3\sqrt[3]{3}\).

Step4: Calculate the product

\(3\times3 = 9\), so \(3\sqrt[3]{81}=9\sqrt[3]{3}\).

Answer:

\(9\sqrt[3]{3}\) (corresponding to the option with \(9\sqrt[3]{3}\))