Answered by Ustadha Naielah Ackbarali
I was wondering why it is obligatory to wash the mouth and nose in ghusl, and whether this has a textual basis or not (in the Quran and Sunnah)

Assalamu aliekum wa rahmatullah
According to the Hanafi school, there are three obligatory actions in the ghusl: washing the mouth, the nose, and the entire body. The proof for this is that Allah Most High has ordered the one who is in a state or ritual impurity (janaba) to purify themselves in Surah Ma’ida verse 6.
“And if you are ritually impure, then purify yourselves thoroughly and completely.”[Qur’an, Surat al-Ma’ida: 6]
The form of this command — fattahharu (‘purify yourselves thoroughly and completely’) — was revealed to us in an emphatic (mubalaga) sense. As such, this is an indication that every part of the body that can be washed without hardship must be washed thoroughly and completely.
In addition, there was no specific restriction stated in this verse of where not to wash. Therefore, since there was no confinement revealed with this action, this would provide reasonable evidence for the necessity of cleansing the mouth and nose in ghusl — as they are possible to wash without hardship. (Mulla Ali al-Qari, Fath al-Bab al-Inaya)
And Allah alone gives success.
Ustadha Naielah Ackbarali
Approved by Faraz Rabbani