Q: We know from the hadith that a woman is not allowed to travel at all a distance more than 3 days and 3 nights (78km) without a mahram. But would this prohibition be relaxed in the case where a female has to acquire deeni knowledge?
Example, in her home town there are absolutely no madrasahs. So a girl travels without a mahram for more than the safar distance and then joins a girls' boarding madrasah and lives there. Will this be permissible under the circumstances?
If not allowed: what is the status of her acquiring knowledge, will her ibaadaat be accepted there, etc?

A: This is not a valid excuse. There are such kitaabs that she can study which are enough to see to her deeni requirements. She can study those kitaabs under the supervision of some senior women in her town or surroundings.
Knowledge is acquired in order that one learns how to obey Allah Ta'ala, it is not learnt to disobey Allah Ta'ala. In travelling alone you are disobeying Allah Ta'ala. So it goes against the purpose of Islamic education. When from the very beginning you are breaking the command of Allah Ta'ala then what good can be expected of such a woman in her future life.
And Allah Ta'ala (الله تعالى) knows best.
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