what is $sqrt3{-729}$?

Explanation:

Step1: Recall cube - root property

The cube - root of a negative number is negative. We need to find a number $x$ such that $x^3=-729$.

Step2: Factorize 729

We know that $729 = 9\times9\times9=9^3$.

Step3: Determine the cube - root

Since $(-9)\times(-9)\times(-9)=-729$, then $\sqrt[3]{-729}=-9$.

Answer:

$-9$