I will Mark you as brainliest if you show your work

  The distance will be about 11 miles . 2) The man's one way-trip will be 5 miles shorter.

Step-by-step explanation:

If the man  drove east by 8 miles and  North by 8 miles and we want to determine the distance that is directly  from east to north then we will use the Pythagorean Theorem  solve for that distance.

Now since we are solving for the distance directly from his home to work we will be looking for the hypotenuse in this case.

a^2 + b^2 =c^2  where c is the hypotenuse

8^2 + 8^2 =c^2

64 +64 = c^2  

c=  

c =  11.31

  In this case the distance from his home directly to his work will be about 11 miles.

2.   To find out how much shorter the man will travel ,add the east and north distance and subtract 11.31 from it.

8 + 8 = 16

16  - 11.31 = 4.69

answer: -2+√x,-2-√x

i hope this , i don't know if you're looking for a pair or not.