Evaluate the sum: 
\[ \sqrt{1 - \frac{1}{2} \cdot \sqrt{1 \cdot 3}} + \sqrt{2 - \frac{1}{2} \cdot \sqrt{3 \cdot 5}} + \sqrt{3 - \frac{1}{2} \cdot \sqrt{5 \cdot 7}} + \dots + \sqrt{40 - \frac{1}{2} \cdot \sqrt{79 \cdot 81}} \]

Let's think step by step and output the final answer within \boxed{}.
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