The expression you provided is:

$\sqrt{(x^2 - 1) - 1}$

Simplifying inside the square root:

1. Combine terms inside the parentheses: $x^2 - 1 - 1 = x^2 - 2$

2. Substitute back: $\sqrt{x^2 - 2}$

Thus, the simplified form of the expression is:

$\sqrt{x^2 - 2}$

Would you like further details or have any questions?

Here are five related questions:

1. How do we find the domain of the expression $\sqrt{x^2 - 2}$?
2. What happens if we square the entire expression $\sqrt{x^2 - 2}$?
3. How would the expression change if we added a constant outside the square root?
4. Can we evaluate $\sqrt{x^2 - 2}$ for specific values of $x$?
5. How would we differentiate the expression $\sqrt{x^2 - 2}$ with respect to $x$?

Tip: When simplifying expressions under a square root, always check if terms can be combined to reduce complexity.