How do I kill horseradish?

Yes it will. But so will mowing it.

https://www.gardeningknowhow.com/edible/herbs/horseradish/control-horseradish-plants.htm

you Brush B Gone directly on the roots

Roundup is toxic so I do not use it. Boiling water or repeated drowning in vinegar will work, will just take a bit longer and repeated treatments.

Roundup will kill it, but you have to wait until it has leaves on it. Roundup won't kill roots. You can also use brush killer.

horseradish if a VERY invasive plant with large root stems that connects with every tinest root near it. It's one of the devil's in your garden and I really don't know how to get rid of it . I am so sorry. Maybe you can go online and ask? Naomie Moore had a good idea.

When we bought our current home there was a meter-square patch of horseradish. I hate the stuff and wanted to put something else there. I soon discovered how hearty it is. Our neighbour, a woman originally from rural Eastern Europe had a patch of a flowering plant I have come to know of as, 'Obedience Plant'. I didn't take notice of it. Resigning myself to a life of pulling horseradish leaves out I focused on pulling. Soon I noticed the obedience plant coming in and taking over. Now several years later, It is a full patch of obedience plant, only a few horseradish plants left. It seems when I pulled the leaves out it gave the obedience plant the opportunity to grow over the spot and suffocate the roots. The obedience plant has a shallow and slightly broad root-like a duck's foot. It offers a nice arrow shaped flower at the end of summer...but it does get rid of horseradish without glyphosate--which is very toxic.

Round Up will kill it but it is toxic so try dumping a gallon of vinegar with a bit of water over top and it is sure to die.