For how long should I boil veggies without compromising or losing its nutrients?
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I usually boil until tender, but that's for potatoes, squash and other big chunks but for leafy greens, just less than 10 mins after boiling. Here's a guide on how long you should boil your veggies http://recipes.howstuffworks.com/tools-and-techniques/how-to-cook-vegetables24.htm
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It depends per vegetable, but I suggest instead to steam or microwave them. By boiling veggies you lose a lot more of their benefits.
It depends which vegetable, but my mom prefers blanching and steaming. This way, veggies are still crunchy and nutritious