उपसर्गादृति धातौ

The वृद्धि is the single substitute when the अ or आ of a preposition (उपसर्ग) is followed by the short ऋ of a verb.
The word आत् is understood here also. When a preposition ending in अ or आ is followed by a root beginning with ऋ, the Vriddhi is the single substitute for the precedent अ or आ and the subsequent ऋ ॥ This debars the guna taught in 6.1.87. Thus उप + ऋच्छति = उपार्च्छति, प्रार्च्छति, उपाध्रोति ॥ Why do we say 'after a preposition'? Observe खट्वर्च्छति, मालर्च्छति, प्रर्च्छकोदेशः = प्रगता ऋच्छका अस्माद् देशात् ॥ Here the word प्र is not treated as an upasarga, hence this sutra does not apply. It is a Gati here. Why do we say 'when ऋ follows'? Observe उप + इत = उपेतः ॥ Why have we used त् after ऋ indicating that short ऋ is to be taken? Observe उप + ऋकारी यति = उपर्कारीयति ॥ No option is allowed here by the subsequent sutra. The त् is used, in fact, for the sake of the subsequent sutra in case of Denominative verbs, no ordinary verb can begin with a long ॠ ॥ Why have we employed the word धातु, when the word 'upasarga' would have caused us to infer its correlative धातु? It is used in order to prevent the application of the rule 6.1.129 which causes प्रकृतिभावः or non-sandhi of ऋ ॥ The repetition of 'Dhatu' shows that the alternative prakriti bhava taught in 6.1.129, would not apply in the case of the ऋ of a Dhatu.