How to Cook Sweet Potatoes Quickly. A quick way to have cooked sweet potatoes is to prick them with a knife or fork several times, then pop them into the microwave.Small sweet potatoes (5-inches long, 2-inches in diameter) take about 3 to 4 minutes to become soft in the microwave. bigger sweet potato (8-inches long, 2-inches in diameter) takes 6 to 8 minutes to become soft. And it's better to microwave two to three small sweet potatoes at one time than trying to cook one big one. Trust me.