Evaluate 
\[\sqrt[\leftroot{-2}\uproot{2}\scriptstyle 3]{-125}\].


The expression you provided is \(\sqrt[3]{-125}\), which represents the cube root of \(-125\).

To solve this, we can express \(-125\) as:

\[
-125 = -5^3
\]

Since the cube root and the cube are inverse operations, the cube root of \(-5^3\) is simply \(-5\):

\[
\sqrt[3]{-125} = -5
\]

Thus, the value of \(\sqrt[3]{-125}\) is \(-5\).

Would you like further details or explanations on this?

Here are 5 related questions for further practice:
1. What is \(\sqrt[3]{27}\)?
2. How do you find \(\sqrt[3]{-64}\)?
3. Can cube roots of negative numbers always be real?
4. What is the cube root of \(8\)?
5. Simplify \(\sqrt[3]{-8} + \sqrt[3]{64}\).

**Tip:** Cube roots of negative numbers are real because odd roots of negative numbers are negative.

Learn how to evaluate the cube root of a negative number, specifically \(\sqrt[3]{-125}\), with step-by-step solutions. This problem involves cube roots, exponentiation, and the cube root theorem, making it suitable for students in Grades 8-10.

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