find the value of 2 multiply ( whole root( mean 2 and root 3 come under one root) 2 plus root 3 minus root 1.5 plus root 2 whole raise to power 2 (excluding 2 outside the bracket)

Let's break down the expression step by step:

1. **Interpret the expression**:
   \[
2 \times \left( \sqrt{2 + \sqrt{3}} - \sqrt{1.5} + \sqrt{2} \right)^2
\]

2. **Simplification strategy**:
   - First, simplify the expressions inside the square root and then evaluate the entire expression.

Let's calculate step by step.The value of the given expression is approximately **9**.

Would you like more details or explanations on the steps? Here are some follow-up questions related to this topic:

1. How do you simplify nested square roots?
2. What is the geometric interpretation of square roots?
3. How does the distribution property apply in this scenario?
4. Can similar expressions be solved using complex numbers?
5. How would the result change if you altered any of the constants?

**Tip**: When working with square roots, always check for possible simplifications before performing further operations.

Learn how to evaluate the expression 2 * (sqrt(2 + sqrt(3)) - sqrt(1.5) + sqrt(2))^2 step by step. This problem involves square roots and exponentiation, suitable for advanced high school students.

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