https://file.aiquickdraw.com/mathbot/file/1724150611947hjzmjx4j.jpg

The expression given in the image is:

\[
D = \sqrt{14 - 2\sqrt{6 - 2\sqrt{6 - 2\sqrt{6 - 2\sqrt{6 - 2\sqrt{6}}}}}}}
\]

Let's simplify it step by step.

### Step 1: Simplify the innermost expression
First, consider the innermost expression:

\[
\sqrt{6}
\]

Since it's just \(\sqrt{6}\), we'll move to the next level:

### Step 2: Substitute the innermost expression back
Now substitute back:

\[
\sqrt{6 - 2\sqrt{6}} 
\]

This expression is already in its simplest form because it involves square roots and is a part of a nested expression.

### Step 3: Continue simplification to the outer expressions
The expression then becomes:

\[
\sqrt{6 - 2\sqrt{6 - 2\sqrt{6}}}
\]

Continuing similarly, but as we notice that the expressions form a recursive pattern. The structure implies that as the pattern continues, it stabilizes or approaches a fixed value.

### Step 4: Solve using recursive patterns
For many similar nested radicals, the pattern often simplifies to a specific integer value, assuming the expressions inside are derived from perfect squares. This results in the whole nested radical simplifying

Explore how to simplify nested radicals step-by-step with detailed explanations and examples. This problem involves nested radicals and their recursive simplification, suitable for advanced high school students and beyond.

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