The expression you provided is:

\[
\frac{3\sqrt{3}}{2} + \sqrt{2}
\]

This expression cannot be simplified further in terms of radicals or integers, so the most simplified form is exactly as it is. If you want to approximate its decimal value, we can calculate:

\[
\frac{3\sqrt{3}}{2} \approx \frac{3 \times 1.732}{2} = \frac{5.196}{2} \approx 2.598
\]
\[
\sqrt{2} \approx 1.414
\]

Now, adding them together:

\[
2.598 + 1.414 = 4.012
\]

Thus, the approximate value of the expression is **4.012**.

Would you like more details or have any further questions?

Here are some related questions:
1. How do you simplify expressions with square roots?
2. How can you rationalize the denominator in radical expressions?
3. What is the difference between exact and approximate values in mathematics?
4. How do you combine radicals in expressions?
5. What are some common rules for simplifying radicals?

**Tip:** When working with radicals, always look to simplify them first before adding or multiplying, but note that unlike regular numbers, radicals can often only be combined under certain conditions.

Learn how to simplify and approximate the expression 3√3/2 + √2. This problem explores key algebraic concepts, such as radicals, simplification, and approximation techniques, providing a detailed solution with decimal values. Suitable for students in Grades 8-10.

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