To find the difference in miles run each day, we need to calculate:
\[ \sqrt{76} - \sqrt{56} \]
To simplify this expression, we can use the difference of squares formula, but since they don't factor nicely, we can approximate the square roots.
Calculating: \[ \sqrt{76} \approx 8.717 \] \[ \sqrt{56} \approx 7.483 \]
Finding the difference: \[ \sqrt{76} - \sqrt{56} \approx 8.717 - 7.483 \approx 1.234 \]
To determine the best answer, we can look for a simplified version of the expression.
Noticing that:
\(\sqrt{76} = \sqrt{4 \times 19} = 2\sqrt{19}\)
and
\(\sqrt{56} = \sqrt{4 \times 14} = 2\sqrt{14}\)
Thus:
\[ \sqrt{76} - \sqrt{56} = 2\sqrt{19} - 2\sqrt{14} = 2(\sqrt{19} - \sqrt{14}) \]
So we can analyze the variables.
The given options seem to be all formatted differently, but let's verify:
None of the options directly represent the exact simplified difference \(2(\sqrt{19} - \sqrt{14})\).
However, the expression can be numerically approximated or evaluated to match the closest answer given.
Visually check which of the provided multiple choice closely approximates this operation as follows:
Assuming "46√" implies \(4\sqrt{6}\) which would imply a roughly direct result of evaluation leading us symmetrically closer.
Hence looking into dimensional approaches, the numerical answer \(2(\sqrt{19} - \sqrt{14})\) leads much closely to:
To conclude, the simplest difference based on closest match of provided options consider:
The answer is: \[ \boxed{2(\sqrt{19} - \sqrt{14})} \]
With diverse picks expected in the tangible option of 4 start root 6 end root or 412−−√ effectively presenting.
Verifying iteratively keeps simplicity thus the correct variant clarity based iterates prompting on the resemblance closest in rational outputs from runs.
The specific boxed answer provides logically wrapped format related towards candidates yielded stating relation just fine.