https://file.aiquickdraw.com/mathbot/file/1724810242930gv1raidx.jpg

the square root is to the power or 3 goes over the x(squared) -1

The expression in the image can be interpreted as:

\[
\sqrt[3]{x^2 - 1} = 2
\]

This is a cubic root equation where the cubic root of \(x^2 - 1\) equals 2.

### Steps to solve the equation:
1. **Isolate the cubic root**:  
   \[
   \sqrt[3]{x^2 - 1} = 2
   \]
   
2. **Cube both sides** to eliminate the cubic root:
   \[
   x^2 - 1 = 2^3
   \]

3. **Simplify** the equation:
   \[
   x^2 - 1 = 8
   \]

4. **Solve for \(x^2\)**:
   \[
   x^2 = 8 + 1
   \]
   \[
   x^2 = 9
   \]

5. **Take the square root** of both sides:
   \[
   x = \pm 3
   \]

### Solution:
The solutions for \(x\) are \(x = 3\) and \(x = -3\).

Would you like more details or have any further questions?

Here are 5 related questions:
1. What happens to the equation if the right side changes to another number, like 4?
2. How would the equation change if it were a square root instead of a cube root?
3. What is the graphical interpretation of this equation?
4. Can you solve similar equations for different powers, such as \(\sqrt[4]{x^2 - 1} = 2\)?
5. What are the steps to solve an equation with a fractional exponent instead of a root?

**Tip:** Always isolate the root or exponent first to simplify solving the equation.

Learn how to solve the equation \(\sqrt[3]{x^2 - 1} = 2\) step-by-step. Understand the concept of cube roots and how to isolate and solve for \(x\). Suitable for high school students and those interested in algebraic equations.

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