Between which two square roots of integers would you find euler's number

Euler's number is an irrational number whose closest value is 2.7182818284590452353602874713527. I say closest because there are still more decimal places added to that. This number was named after Leonhard Euler. Because the lengthy numbers are very inconvenient, it is conventionally assigned as letter 'e'.

Let's just shorten the value of Euler number to 2.718. We can estimate that this number is placed between the perfect squares,4 and 9. But where exactly? The only way to know this is find the square roots of all integers (or whole numbers) between 4 and 9. Then, see which region does e belong to. After trial-and-error process, the answer is between the square roots of 7 and 8. Particularly, the values are between 2.646 and 2.828.