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The result of the expression \( 2 \cdot a - b \), where \( a = 1 + \sqrt{2} - \sqrt{3} \) and \( b = \sqrt{4} + \sqrt{8} - \sqrt{12} \), is 0.

Would you like further details on how this result was derived? Here are five related questions to explore:

1. How do you simplify expressions involving square roots?
2. What are the common properties of square roots and radicals?
3. Why does \( \sqrt{12} \) simplify to \( 2\sqrt{3} \)?
4. How would you calculate \( 3a - 2b \) using similar methods?
5. What is the geometric interpretation of this type of algebraic simplification?

**Tip:** When simplifying expressions with square roots, always check if the terms inside the roots can be factored for further simplification.

Dacă a = 1 + √2 - √3 și b = √4 + √8 - √12, calculați 2 · a - b.

Solve the expression 2a - b where a = 1 + √2 - √3 and b = √4 + √8 - √12. Learn about simplifying radicals and applying properties of square roots in this detailed solution for high school algebra students.

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