In plain words
Buddhi does not mean merely the power of thinking. It is not merely the power of inquiry. It is not merely the power of Viveka. It is not merely the power of Vijñāna. It is the power of inquiry joined with the power of discrimination. On the strength of their debate, Ubhaya Bhāratī accepted Maṇḍana Miśra's defeat. That is, she accepted that her own husband had lost. This was a decision joined with Satya and Ṛta. Śaṅkara was very glad of it. Nor did she stop there; Ubhaya Bhāratī commanded him, "By this decision you must become Śaṅkara's servant, you must become his disciple; take sannyāsa." The word is Satya. To do what you have said is Satya. To say what you have thought, and to do what you have said, is Ṛta. So Ubhaya Bhāratī commanded him, "Take this sannyāsa in keeping with this decision." But she had received, in the householder's Dharma, the titles of lady of the house, partner in Dharma and Lakṣmī of the home; and wishing to give the women of the world an ideal, Ubhaya Bhāratī thought it natural that when her husband became a sannyāsī she too should become one, and she too took sannyāsa. To follow her husband is natural for a wife. She had no real need to take sannyāsa. But she took sannyāsa for the sake of an ideal for the world. Ubhaya Bhāratī was a woman of pure heart. She built herself an āśrama and made a resolve to show the right path to people full of Ahaṅkāra, who long to win victory by brain power alone.
Having built her āśrama, she set out from it one day with some of the women disciples who followed her, to bathe in the river. Midway along the road a sannyāsī, famed as one who had given up every attachment, had a dried gourd for drinking water; afraid that someone might steal it if he left it out anywhere, and out of his attachment to it, this sannyāsī lay down with that gourd under his head. Ubhaya Bhāratī resolved to give him the right teaching. So that he could hear, she said to her disciples: 'Look! He has given up every attachment, but his attachment to the gourd has not gone. When there is this much attachment to so small and trifling a thing, how grandly his attachment to great things must have gone! This conduct does not fit his name!' This man who had given up every attachment heard it. Pain and anger both filled his heart.