To find the best decimal approximation for \(\sqrt{60}\), we can estimate the value.
First, we know that:
- \( \sqrt{49} = 7 \)
- \( \sqrt{64} = 8 \)
Since 60 is between 49 and 64, \(\sqrt{60}\) should be between 7 and 8.
Now, to refine our estimate further, we can guess some values that are closer to \(\sqrt{60}\):
- \( 7.7^2 = 59.29 \)
- \( 7.8^2 = 60.84 \)
- \( 7.75^2 = 60.0625 \)
- \( 7.73^2 = 59.5929 \)
From these calculations:
- \( 7.7^2 \) is slightly less than 60.
- \( 7.75^2 \) is very close to 60 (60.0625).
- \( 7.73^2 \) is also less than 60 but closer than 7.7.
Since \( 7.75 \) gives us \( 60.0625 \) which is quite close to \( 60 \), and considering the closeness of the squares, the best decimal approximation for \(\sqrt{60}\) from the options provided would be \( \mathbf{7.75} \).