How can I vacuum a rug with long fluffy yarns. It's too large to shake outside.?

Select the best vacuum for your type of carpet

Shaw recommends using vacuums with a rotating brush or combination beater/brush bar that agitates the carpet pile and mechanically loosens soil for removal. Carpet with thick loop pile construction, particularly wool and wool-blend styles, may be sensitive to brushing or rubbing of the pile surface and may become fuzzy. In addition, shag (or cabled) styles with long pile yarns tend to wrap around the rotating brushes causing damage to the yarn. For these products, Shaw recommends a suction-only vacuum or a vacuum with an adjustable brush lifted away from the carpet so it does not agitate the pile. Be sure to test a vacuum with a beater/brush bar in an inconspicuous location before regular use, to make sure it doesn't produce excessive fuzzing.

A vacuum with a beater bar attachment.

Most people use a Vacuum.

Set it for "Shag".

Go over it two or three times. Cross-Patching. (ie. in different directions each pass.)

You can. but it's a hassle