Evaluating Nested Square Root Expression

The problem requires simplifying the following nested radical expression:

$ \sqrt{93 + \sqrt{32 + \sqrt{274 + \sqrt{225}}}} $

We simplify this expression by working from the inside out.

Innermost Calculation

First, calculate the square root of the innermost number:

$ \sqrt{225} = 15 $

Second Layer Calculation

Substitute this result back into the expression:

$ \sqrt{274 + 15} $

Now, calculate this new square root:

$ \sqrt{289} = 17 $

Third Layer Calculation

Substitute this result back:

$ \sqrt{32 + 17} $

Calculate the square root:

$ \sqrt{49} = 7 $

Outermost Layer Calculation

Finally, substitute this result into the outermost part:

$ \sqrt{93 + 7} $

Calculate the final square root:

$ \sqrt{100} = 10 $

Final Result

The evaluated value of the expression $ \sqrt{93 + \sqrt{32 + \sqrt{274 + \sqrt{225}}}} $ is 10.