Question

find the value of $sqrt3{-216}$.

Explanation:

Step1: Recall cube root property

For negative numbers, $\sqrt[3]{-a} = -\sqrt[3]{a}$ where $a>0$.
So $\sqrt[3]{-216} = -\sqrt[3]{216}$

Step2: Find cube root of 216

We know $6^3 = 6\times6\times6 = 216$, so $\sqrt[3]{216}=6$.

Step3: Apply the negative sign

Substitute back: $-\sqrt[3]{216} = -6$

Answer:

$-6$