To solve the equation $4x^2 - 72 = 0$ using the square root property, let's follow these steps:

Step-by-Step Solution

1. Isolate the $x^2$ term: $4x^2 = 72$

2. Divide both sides by 4 to simplify: $x^2 = 18$

3. Apply the square root property: Since $x^2 = 18$, we can take the square root of both sides. Remember to consider both the positive and negative square roots: $x = \pm \sqrt{18}$

4. Simplify $\sqrt{18}$: $\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$ Thus, we have: $x = \pm 3\sqrt{2}$

Final Answer

$x = 3\sqrt{2} \quad \text{or} \quad x = -3\sqrt{2}$

Would you like more details on any of these steps, or do you have any questions?

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Here are some related questions that expand on this concept:

1. How would you solve $5x^2 - 125 = 0$ using the square root property?
2. What is the square root property, and why is it useful for certain quadratic equations?
3. How do we simplify expressions like $\sqrt{18}$, and are there general rules for simplifying square roots?
4. Can all quadratic equations be solved using the square root property?
5. What is the difference between solving quadratics by factoring versus using the square root property?

Tip: When using the square root property, make sure to isolate the squared term before taking the square root, and remember to account for both the positive and negative roots.