What is the value of  m
 , if  m⎯⎯⎯√3=−8
 ?

We are given the equation:

\[
\sqrt[3]{m} = -8
\]

This means that the cube root of \( m \) is equal to \(-8\). To solve for \( m \), we need to cube both sides of the equation:

\[
m = (-8)^3
\]

Now calculate the cube of \(-8\):

\[
m = -8 \times -8 \times -8 = -512
\]

Thus, the value of \( m \) is:

\[
m = -512
\]

Would you like further details or have any other questions?

Here are some related questions:
1. How do cube roots differ from square roots?
2. What happens when cubing a negative number?
3. Can cube roots of negative numbers have complex solutions?
4. How would you solve \( \sqrt[4]{m} = 8 \)?
5. What are the properties of cube root functions?

**Tip:** The cube root of a negative number is always negative.

Learn how to solve the cube root equation m^(1/3) = -8 with a step-by-step explanation. This problem explores cube roots, exponents, and the cube root theorem, suitable for students in Grades 8-10.

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