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How to cook vegetables? Cook the beetroot and carrots with the potatoes in different pots in boiling water until tender. It takes 15-20 minutes to cook potatoes and carrots. For boiling beets - 1-1. 5 hours, depending on its size. Check your readiness with a sharp knife - it should easily pierce the root crop. Drain the water, and cool the vegetables. Peel the cooled potatoes, carrots and beets. Rub them separately on a medium grater.