To solve the equation 

\[
\frac{3x^2}{3} = \frac{2}{3},
\]

we can simplify and isolate \(x^2\). Here's the step-by-step solution:

1. **Simplify** the left side by canceling out the 3 in the numerator and the denominator:

\[
x^2 = \frac{2}{3}.
\]

2. **Solve for \(x\)** by taking the square root of both sides. Remember to include both the positive and negative roots:

\[
x = \pm \sqrt{\frac{2}{3}}.
\]

3. **Simplify the square root**. To simplify \(\sqrt{\frac{2}{3}}\), we can rewrite it as:

\[
x = \pm \frac{\sqrt{2}}{\sqrt{3}}.
\]

4. **Rationalize the denominator** by multiplying both the numerator and the denominator by \(\sqrt{3}\):

\[
x = \pm \frac{\sqrt{2} \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \pm \frac{\sqrt{6}}{3}.
\]

### Solution

The solutions to the equation \(\frac{3x^2}{3} = \frac{2}{3}\) are:

\[
x = \frac{\sqrt{6}}{3} \quad \text{and} \quad x = -\frac{\sqrt{6}}{3}.
\]

Would you like more details, or do you have any questions?

Here are some related questions that might interest you:

1. What if the equation was \(\frac{3x^2}{3} = 3\)?
2. How do we solve \(3x^2 = 2\) without fractions?
3. How do we handle square roots when they appear in the denominator?
4. What is the difference between simplifying square roots and rationalizing them?
5. How would the solution change if the equation had a different coefficient for \(x^2\)?

**Tip:** Always remember to include both the positive and negative solutions when solving for \(x\) by taking the square root of both sides of an equation.

Learn how to solve the equation 3x^2/3 = 2/3 with a detailed step-by-step solution. This problem involves simplifying fractions, solving quadratic equations, and understanding square roots. Suitable for students in Grades 7-9.

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