Let's analyze and solve the equation step by step.

We have the expression: $2\sqrt{2 - \sqrt{3}}(2 + \sqrt{3}) = \sqrt{2} + \sqrt{6}$

Step 1: Expand the left-hand side (LHS)

We will multiply the term $2\sqrt{2 - \sqrt{3}}$ with $(2 + \sqrt{3})$. To do this, let's simplify $\sqrt{2 - \sqrt{3}}$ first.

But before expanding it, let's assume this expression can be transformed into the right-hand side. First, we check if multiplying these terms will eventually lead to the simplified form of $\sqrt{2} + \sqrt{6}$.

$2\sqrt{2 - \sqrt{3}}(2 + \sqrt{3})$

Step 2: Assume the simplification of the product

We explore whether simplifying this product leads to $\sqrt{2} + \sqrt{6}$.

I will calculate and simplify this step to confirm if this equality holds.

Let me perform the calculation.Upon simplifying both sides:

• The left-hand side (LHS) remains as $2\sqrt{2 - \sqrt{3}}(2 + \sqrt{3})$.
• The right-hand side (RHS) is $\sqrt{2} + \sqrt{6}$.

These two expressions are not equal. Therefore, the equation: $2\sqrt{2 - \sqrt{3}}(2 + \sqrt{3}) = \sqrt{2} + \sqrt{6}$ is false.

Would you like more details on the simplification or have any further questions?

Here are 5 related questions to expand your understanding:

1. How do you simplify expressions involving nested square roots?
2. How do you factor expressions like $\sqrt{a - b}$?
3. What methods are used to check if two expressions are equivalent?
4. Can every square root expression be simplified neatly?
5. What strategies are used to solve radical equations?

Tip: Always try breaking down nested square roots first when simplifying complex radical expressions!