The square root of 765 is approximately $27.66$.

Would you like further details or have any questions? Here are some related questions to consider:

1. What is the square of 27.66?
2. How do you calculate square roots by hand?
3. What is the square root of a perfect square near 765?
4. Can you calculate cube roots using a similar method?
5. How does estimating square roots differ for non-perfect squares?

Tip: When dealing with square roots of non-perfect squares, you can estimate them by finding the nearest perfect squares as a reference.