The image contains a mathematical expression in Arabic. Here's the simplified and step-by-step interpretation:

The expression can be translated and simplified as follows:

1. It appears as a nested square root sequence of numbers: $\sqrt{2 - \sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2}}}}}$

Step-by-Step Solution:

Start from the innermost term:

1. Simplify $\sqrt{2}$: \text{It's just \sqrt{2}.}

2. Add 2: $2 + \sqrt{2}$

3. Take the square root of that: $\sqrt{2 + \sqrt{2}}$

4. Repeat this process outward until the entire expression is simplified: $\sqrt{2 - \sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2}}}}}$

Numerical Approximation:

Let’s calculate step by step:

1. $\sqrt{2} \approx 1.414$
2. $2 + \sqrt{2} \approx 2 + 1.414 = 3.414$
3. $\sqrt{3.414} \approx 1.847$
4. Repeat for the next terms:
   • $2 + 1.847 = 3.847$
   • $\sqrt{3.847} \approx 1.961$
   • $2 - 1.961 = 0.039$
   • Final square root: $\sqrt{0.039} \approx 0.197$

Thus, the approximate numerical result is 0.197.

Would you like further explanations or details?

Questions to Expand Your Knowledge:

1. What is the convergence behavior of nested radicals like this one?
2. How can you simplify nested square roots algebraically?
3. Why do these nested expressions sometimes converge to specific values?
4. What happens if the sequence alternates between addition and subtraction?
5. Can this be generalized to different numbers other than 2?

Tip:

Always work from the innermost part of a nested radical outward to avoid confusion and ensure clarity in calculations.