Eradicating Horseradish

in Fruit & veg
we made the terrible mistake of planting a Horseradish in our raised vegetable bed last year. It became a monster and we got rid of it. It was so deeply rooted that we could not get every bit out and it has come back with a vengance. Do we have to dig it all out or could we apply a systemic weed killer ? Would it be safe to use such a weed killer on our veggie patch?
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If you only paint the leaves with a glyphosate gel, that should work. It is safe in a veggie patch, it decomposes when it hits the soil. It is not persistent in the soil and will not affect future crops. Otherwise, dig it up once a year, use the root, and hey presto next year you have another one.
It keeps sprouting up amongst all of our crops so I will investigate the glyphosate gel. Digging it out would be a nightmare. We tried it before and went down one metre into solid clay, but we still didn't manage to get all of it. Never want to eat the stuff again!