To find the approximate values between which \(\sqrt{40}\) falls, we can first calculate some perfect squares:
- \(6^2 = 36\)
- \(7^2 = 49\)
From this, we can see that:
\[ 6^2 < 40 < 7^2 \]
This means:
\[ 6 < \sqrt{40} < 7 \]
Therefore, \(\sqrt{40}\) is between \(6\) and \(7\).
So the answer is:
\[ \text{between 6 and 7.} \]