Question

Jake runs 76–√ miles on Monday and 56–√ miles on Tuesday. What is the difference in miles run each day?(1 point)
Responses

46–√
4 start root 6 end root

212−−√
2 start root 12 end root

26–√
2 start root 6 end root

412−−√

Answer 1

To find the difference in miles run each day, we need to calculate the absolute difference between the two distances Jake ran:

Jake runs \( \sqrt{76} \) miles on Monday and \( \sqrt{56} \) miles on Tuesday.

The difference is given by:

\[
\left| \sqrt{76} - \sqrt{56} \right|
\]

To compute this value, we can simplify \( \sqrt{76} \) and \( \sqrt{56} \):

1. **Simplifying \( \sqrt{76} \)**:
\[
\sqrt{76} = \sqrt{4 \times 19} = \sqrt{4}\sqrt{19} = 2\sqrt{19}
\]

2. **Simplifying \( \sqrt{56} \)**:
\[
\sqrt{56} = \sqrt{4 \times 14} = \sqrt{4}\sqrt{14} = 2\sqrt{14}
\]

Now substituting back, the difference is:

\[
\left| 2\sqrt{19} - 2\sqrt{14} \right| = 2 \left| \sqrt{19} - \sqrt{14} \right|
\]

Since \( \sqrt{19} > \sqrt{14} \), we can remove the absolute value:

\[
2(\sqrt{19} - \sqrt{14})
\]

This result does not directly match any of the options you've given. However, if you were looking for just the expression \( \sqrt{76} - \sqrt{56} \), we would have \( 2(\sqrt{19} - \sqrt{14}) \).

Since it looks like we're asked for a numerical difference, approximating the square roots:

- \( \sqrt{76} \approx 8.717 \)
- \( \sqrt{56} \approx 7.483 \)

Thus,

\[
\sqrt{76} - \sqrt{56} \approx 8.717 - 7.483 \approx 1.234
\]

None of your options seem to match the calculations strictly either.

Please clarify if you want to stick to the algebraic expression or adapt with numerical approximations.