How to grow beetroot at home without seeds?
Growing beetroot without seeds is possible by regrowing from beet tops! While you won't get full-sized roots, you'll get delicious greens:
Save the top 1-2 inches of beetroot with the crown intact. Place cut side down in shallow water, changing water every 2-3 days. Once roots develop and new green growth appears (about 1-2 weeks), transplant to soil.
Plant so the crown is just above soil level. Keep consistently moist. You'll get a continuous harvest of beet greens that taste similar to spinach or chard. The leaves are packed with nutrients!
For actual beet roots, you need to grow from seed, but regrowing tops gives you bonus greens from kitchen scraps. It's a fun project, especially with kids!
The greens will keep producing for several months if you harvest outer leaves regularly. They're great in salads or cooked like spinach.
Regrow Vegetables guide has specific regeneration techniques!