Question

find the value of \\(\sqrt3{-1000}\\).

Explanation:

Step1: Recall the property of cube roots

For any real number \( a \), \( \sqrt[3]{-a}=-\sqrt[3]{a} \). So we can rewrite \( \sqrt[3]{-1000} \) as \( -\sqrt[3]{1000} \).

Step2: Find the cube root of 1000

We know that \( 10\times10\times10 = 10^3=1000 \), so \( \sqrt[3]{1000}=10 \).

Step3: Combine the results

Since \( \sqrt[3]{-1000}=-\sqrt[3]{1000} \) and \( \sqrt[3]{1000}=10 \), then \( \sqrt[3]{-1000}=- 10 \).

Answer:

\(-10\)