find the value of $sqrt3{216}$.

Explanation:

Step1: Recall cube - root definition

The cube - root of a number (x), denoted as (\sqrt[3]{x}), is a number (y) such that (y^3=x). We need to find a number (y) where (y^3 = 216).

Step2: Factorize 216

We know that (216=6\times6\times6), i.e., (216 = 6^3).

Step3: Find the cube - root

Since (\sqrt[3]{216}=\sqrt[3]{6^3}), by the property (\sqrt[3]{a^3}=a), we have (\sqrt[3]{216}=6).

Answer:

6