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As-salamu ´alaykum Sayyidi Abu Dahdah,

In the Shafi´i school your Salah is sound even if you leave out the Surah. In addition, as you know, sajda as-sahw is recommended, and leaving it out would not render your Salah invalid (if leaving out the Surah had necessitated it in the first place, which it does not). As you may know, the opinion of al-Imam ash-Shafi´i (rahmatu'Allahi ´alayh) himself is that it is Sunnah to recite a second Surah in all raka´at. And this is the reported practice of Sayyidina Abu Bakr as-Siddiq (radiya'Allahu ´anh). As for the remaining schools; in the Maliki math'hab you will find the opinion that the second Surah is Wajib in the first two raka´at, supporting themselves with the Hadith of there not being a prayer without Fatihat al-Kitab, with the addition "and a Surah after it".

wa'Llahu a'lam