Sakura had a desire to become stronger, as she was tired of relying on Naruto. Tsunade agreed to train her.
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Tsunade because sakura is still in training but there are hints that say that once shes older she will be the new tsunade if not stronger
Sakura and Ino was (in part1) about ecual in strength, but in Shippuden, Sakura is stronger than Ino. Ino's total stat is 21 and Sakura's stat is 26. Sakura gained enough strength and beauty thanks to Tsunade. Jiraiya said that Tsunade did a good job in making a younger Tsunade and Kakashi even said Sakura can surpass tsunade.
Sakura asks Tsunade to train her in episode 141.
there both the same age :)
She trains with Tsunade and she learns medical skills but by combining her medical and taijutsu she gets super strength like Tsunade