To find the difference in miles run by Jake on Monday and Tuesday, we need to calculate:
\[ \sqrt{76} - \sqrt{56} \]
First, let's approximate the square roots:
-
For \(\sqrt{76}\):
- \( \sqrt{76} = \sqrt{4 \cdot 19} = 2\sqrt{19} \)
-
For \(\sqrt{56}\):
- \( \sqrt{56} = \sqrt{4 \cdot 14} = 2\sqrt{14} \)
Now we can express the difference:
\[ \sqrt{76} - \sqrt{56} = 2\sqrt{19} - 2\sqrt{14} = 2(\sqrt{19} - \sqrt{14}) \]
We can evaluate the approximate values of \(\sqrt{19}\) and \(\sqrt{14}\):
- \(\sqrt{19} \approx 4.36\)
- \(\sqrt{14} \approx 3.74\)
Thus,
\[ \sqrt{19} - \sqrt{14} \approx 4.36 - 3.74 = 0.62 \]
Now multiplying by 2 gives:
\[ 2(0.62) = 1.24 \]
This does not directly match any of the options listed, indicating we need to look for a more simplified term.
However, if we take it step by step without approximating:
The difference in a squared form can also be solved by rationalizing and simplifying:
Returning to \( \sqrt{76} - \sqrt{56} \):
- Square both results to find if any manipulations yield the responses given
- So \(76 - 56 = 20\), where some manipulation gives \(\sqrt{20} = 2\sqrt{5}\), indicative of 4 options we do see.
The closest matching answer among your selections to \( \sqrt{76} - \sqrt{56} \) will be computed or double-checked being:
Taking a guess from approximations will help lead us to Option:
\[ 2\sqrt{12} \]
This requires direct coefficient simplification since squared results lead to further simplifications to help isolate the values straightforward. Backtrack to articulate answer:
Thus the output difference is likely expressed in option providing:
Conclusion: Answering choice is \(2\sqrt{12}\).
1 answer