Why does the `请` take two duplicate words on its verb occasionally (e.g. `请洗洗你的袜子`) I've read these sentences in my Rosetta Stone courses:

请洗洗你的袜子
请洗一下楼梯


However, why does the first sentence use two 洗 consecutively before taking the object? Also, how can I tell when to use one verb and when to use two verbs?

And finally, does the 请洗你的袜子 make sense in Mandarin? If that does make sense and is used often, what's the difference between the two?
quotation from 外国人实用汉语语法：
(1) the reduplication of a verb implies a short and quick 
action 

(2) expresses an attempt or trial

(3)expresses a sense of being light and relaxed

and the same goes for  [verb] +一下 

请洗你的袜子 seems to make sense in Mandarin