How Can I Make Pureed Soups Without a Blender?

Q: I was introduced to the wonders of carrot soups during college and would love to make some myself! Unfortunately, every carrot soup recipe I come across seems to require a blender, which I don’t have (and purchasing one is not in the budget). How can I make tasty carrot and squash soups without one? Would grating the carrots before putting them in the soup be a good substitute? This also applies to pumpkin/squash soups.

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