Bhashya
र्मिति, तत् एतावदेवेति विज्ञेयं त्वया- इति ह एवं किल अमृतत्वसाधनमात्मज्ञानं प्रियायै भार्यायै उक्त्वा याज्ञवल्क्यः- किं कृतवान्? यत्पूर्वं प्रतिज्ञातम् 'प्रव्रजिष्यन्नस्मि' इति, तच्चकार, विजहार प्रव्रजितवानित्यर्थः ।परिसमाप्ता ब्रह्मविद्या संन्यासपर्यवसाना ।एतावान् उपदेशः, एतत् वेदानुशासनम्, एषा परमनिष्ठा, एष पुरुषार्थकर्तव्यतान्त इति ॥
In plain words
'...the knower.' 'That is all there is to know,' he told her. And having given his beloved wife this one means to immortality — knowledge of the Self — what did Yājñavalkya do next? Exactly what he had vowed earlier: 'I am about to go forth.' He did it. He left, and became a wandering renunciant. The knowledge of brahman is now complete, and it ends in renunciation. This much is the whole teaching. This is what the Veda itself instructs. This is the highest ground there is to stand on. This is where every human aim finally comes to rest.
Close to the Sanskrit
'...the knower' — thus [ends the passage]. 'That much alone is to be known by you' — thus. So indeed, having spoken this means of immortality, the knowledge of the Self, to his beloved wife, what did Yājñavalkya do? What he had earlier vowed, 'I am about to go forth,' that he did: he departed, meaning he went forth as a renunciant. The knowledge of brahman is completed, culminating in renunciation. This much is the teaching; this is the Veda's own instruction; this is the highest state; this is the final end of the duties that make up human aims.