Using processor fitted with shredder attachment, shred horseradish.
Transfer horseradish to medium bowl.
Fit processor with metal blade.
Return horseradish to work bowl and add ingredients. Process until almost smooth, scraping down sides of bowl occasionally, about 5 minutes. Mix in salt.
Place horseradish in glass jar. Cover tightly; chill at least 1 day and up to 10 days.
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