There are many great reasons for you to eat sprouts. They are very nutritious and come in a wide variety of flavors for you to add to any dish you like. You can sprout anything from the standard mung bean to onions, garlic or radish for some extra kick. It is a pretty easy process depending on which seeds you choose to sprout and they benefits are huge.
By taking grains, beans, nuts and seeds and sprouting them, you are actually making them far easier to digest and absorb the nutrients from them. When these seeds are in the sprouting stage, they are packed with nutrients that are easily accessible to your body. These sprouts also have a lower glycemic index and have increased levels of vitamins, antioxidants, enzymes, amino acids and essential fatty acids. The proteins in the sprouts are a much higher quality and there is a much greater fiber content in the sprouts than that of just the seeds. If you think about it, a seed is a lot like an egg. It has a protective coating, a center part which will become the new life, and between the two there is a layer of nutrient waiting there for the new life to feed on as it begins to grow. None of which does you any good when you just munch on seeds because you can't get to the nutrient part.
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I should also mention that you will often find things like mung bean sprouts cooked in a stir fry. Cooking your sprouts kills much of the nutrients you have just created by sprouting them. You can do it, but it is much, much better to simply eat them raw and fresh. Really, all vegetables and fruits cooked are less nutritious than eating them raw, but not everyone has the palette for raw foods. I will often make a stir fry and just lightly cook my vegetables and then throw in the sprouts uncooked to the warm stir fry just to warm them a little. I eat them right out of the sprouter, so they generally aren't cold anyways.