find the value of $sqrt3{-125}$.

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 $y$ where $y^3=- 125$.

Step2: Factorize - 125

We know that $125 = 5\times5\times5=5^3$, and $-125=(-5)\times(-5)\times(-5)=(-5)^3$.

Step3: Determine the cube - root

Since $(-5)^3=-125$, then $\sqrt[3]{-125}=-5$.

Answer:

$-5$