I-705  Washington (link)

1.50 miles [1]; serves Tacoma. Opened in 1990.

If you're not from the Emerald City, knowing that True Seattlites derogate Tacoma at every opportunity will add needed context to this 1998 Seattle Times story:

"TACOMA - Interstate 705 skirts the eastern edge of downtown, separating the decaying central business district from an equally dilapidated port and waterfront. Calling it an interstate inflates the freeway's importance. It is all tentacles reaching out every which way, appearing to search for some thriving commerce to justify its exit ramps." [2]

I-705 is short enough to easily overlook. Witness the following misc.transport.road exchange (about states with no odd 2-digit interstates):

Van Isaac Anderson wrote:
>Ken Knutson wrote:
>> "Andy P. Jung" wrote:
>
>> >In the Continental US and excluding
>> > Washington, D.C., we have:
>> >
>> >Nebraska
>> >
>> >Did I miss any?
>> 
>> Washington State.  Seven Interstates 
>> -- 5, 82, 90, 182, 205, 405, 705
>> -- none 2-digits/odd.
>
>Being a Washingtonian, I must say that your list
>astounds me.  I've never heard of 705, nor can
>I figure out where it might be (besides
>along I-5 somewhere).  Would you please divulge
>the location of this interstate? (I don't have
>my official Washington State Highway map yet)

See also: I-705 (Paul Henry)

Sources

1. Route Log and Finder List - Interstate Highways, FHWA, Oct. 31, 2002.
2. "In the 6th District, Dicks keeps delivering." Seattle Times, March 29, 1998.