getting rid of horseradish

You could leave as much foliage on as possible up to september and then treat this with glyphosate. This is the best time to apply it as the plant draws sugars back down from it's leaves and into its roots. Glyphosate being a sugar is pulled down too killing it.

Without a digger - the short answer is - you can't!!!! LOL Take it from one who tried for years and eventually had to pay out a lot of money to replace the drains it had broken into!!!
Seriously though - I will be as interested as you to find out the answer as it can be a thug and I was advising a previous questioner to keep it in a large pot etc to avoid invasion! I am sure these erudite GOYers will have an answer...finger crossed!