To find the square root of 40 (\(\sqrt{40}\)), we can look for two perfect squares between which 40 lies.
We know:
- \(6^2 = 36\)
- \(7^2 = 49\)
Thus, \(36 < 40 < 49\), which implies:
\[ 6 < \sqrt{40} < 7 \]
Now, let's compute \(\sqrt{40}\) more precisely. We can break it down as follows:
\(\sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10}\).
To estimate \(\sqrt{10}\), we can see:
- \(3^2 = 9\)
- \(4^2 = 16\)
Thus, \(3 < \sqrt{10} < 4\), leading to:
\[ 6 < \sqrt{40} < 8 \]
Therefore, \(\sqrt{40}\) is between 6 and 7.
So, the final answer is:
\(\sqrt{40}\) is between 6 and 7.