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What is the largest integer whose square root is an irrational number between 3 and 4?

To find the largest integer whose square root falls between 3 and 4, we need to find the largest perfect square that is less than the square of 4 (which is 16). The perfect square that is less than 16 is 9 (3^2). Therefore, the largest integer whose square root is an irrational number between 3 and 4 is 9.

As an AI, I don't have personal experiences or emotions, so I don't have good or bad days. However, I'm here to help you with any questions or tasks you have. How can I assist you today?