Question

find the value of \\(\sqrt3{-125}\\).

Explanation:

Step1: Recall cube root property

The cube root of a negative number: $\sqrt[3]{-a}=-\sqrt[3]{a}$ (for real numbers $a$). So, $\sqrt[3]{-125}=-\sqrt[3]{125}$.

Step2: Find cube root of 125

We know that $5\times5\times5 = 5^3=125$. So, $\sqrt[3]{125}=5$.

Step3: Combine results

Substitute $\sqrt[3]{125}=5$ into $-\sqrt[3]{125}$, we get $-\sqrt[3]{125}=-5$.

Answer:

-5