A man starts walking from home and walks 4 miles east, 4 miles southeast, 7 miles south, 6 miles southwest, and 2 miles east. How far has he walked?
23 $\mathrm{mi}$
If he walked straight home, how far would he have to walk? (Round your answer to three decimal places.)
$\mathrm{mi}$

Step 1 ：The man has walked a total of 23 miles in different directions.

Step 2 ：To find out how far he would have to walk if he went straight home, we need to calculate his displacement from his home. This involves breaking down each direction into its component parts (north/south and east/west).

Step 3 ：East and west are opposite directions, so we subtract the distance walked west from the distance walked east. Similarly, north and south are opposite directions, so we subtract the distance walked south from the distance walked north.

Step 4 ：Calculating the components, we get: east = 8.82842712474619 miles, southeast = 4 miles, south = 14.071067811865476 miles, southwest = 6 miles, west = 4.242640687119286 miles.

Step 5 ：Subtracting the west component from the east component, we get: east_west = 4.585786437626904 miles.

Step 6 ：Subtracting the north component from the south component, we get: north_south = 14.071067811865476 miles.

Step 7 ：Then, we use the Pythagorean theorem to calculate the straight-line distance from the man's current location to his home. This gives us: straight_home = 14.79947251146606 miles.

Step 8 ：Final Answer: The man has walked a total of 23 miles. If he walked straight home, he would have to walk approximately \(\boxed{14.799}\) miles.