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If you are having the hysterectomy performed for a benign (non-cancerous) condition, then you can choose to keep your ovaries. If the ovaries appear healthy, your surgeon will leave them intact (removal is done if they are unhealthy or look abnormal). Removal of ovaries will lead to early onset of menopause and also severe menopausal symptoms since the estrogen production will not be present. Leaving the ovaries intact also helps you to reduce risk for osteoporosis and heart disease. For detailed discussion visit your gynecologist before undergoing the procedure.
Take care.