The inequality you've provided is:

$n^2 > 3$

To solve for $n$, we can approach this by taking the square root of both sides.

1. Take the square root of both sides: $\sqrt{n^2} > \sqrt{3}$

2. This simplifies to: $|n| > \sqrt{3}$

Since the absolute value of $n$ must be greater than $\sqrt{3}$, we have two possible solutions:

$n > \sqrt{3} \quad \text{or} \quad n < -\sqrt{3}$

Therefore, the solution to the inequality is:

$n > \sqrt{3} \quad \text{or} \quad n < -\sqrt{3}$

Where $\sqrt{3} \approx 1.732$. Thus:

$n > 1.732 \quad \text{or} \quad n < -1.732$

Let me know if you'd like further explanation or any clarifications!

Related Questions:

1. What is the value of $\sqrt{3}$ and how is it approximated?
2. How can inequalities involving squares be solved algebraically?
3. What is the significance of absolute value in solving inequalities like this?
4. How would the inequality change if the expression was $n^2 \geq 3$?
5. Can we graph this inequality on the number line? What does it look like?

Tip:

Whenever you see an inequality with a squared variable, remember to consider both the positive and negative roots because the square of a number is always positive.