Use the Square Root Property to solve the equation. (Enter your answers as a comma-separated list.)

3*x*2 = 225

To solve the equation \( 3x^2 = 225 \) using the Square Root Property, follow these steps:

### Step 1: Isolate the squared term
First, we need to isolate the \( x^2 \) term by dividing both sides of the equation by 3:
\[
x^2 = \frac{225}{3}
\]
\[
x^2 = 75
\]

### Step 2: Apply the Square Root Property
The Square Root Property states that if \( x^2 = a \), then \( x = \pm \sqrt{a} \).

Applying this property to our equation:
\[
x = \pm \sqrt{75}
\]

### Step 3: Simplify the square root
The square root of 75 can be simplified:
\[
\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}
\]

So, the solutions are:
\[
x = \pm 5\sqrt{3}
\]

### Final Answer
The solutions to the equation are:
\[
\boxed{5\sqrt{3}, -5\sqrt{3}}
\]

Do you want more details, or have any questions about this?

Here are five related questions:
1. How do you solve quadratic equations using the quadratic formula?
2. What are the steps to simplify square roots?
3. How do you solve equations by completing the square?
4. What is the geometric interpretation of solutions to \( x^2 = a \)?
5. How do you solve quadratic equations by factoring?

**Tip:** When using the Square Root Property, always remember to include both the positive and negative roots.

Learn how to solve the equation 3x^2 = 225 using the Square Root Property with a detailed step-by-step solution. This problem covers key algebraic concepts, including quadratic equations and the Square Root Property theorem. Suitable for students in Grades 7-9.

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