The root of نَصَرَ consists of nūn, ṣād, rāʾ. Replace the three placeholders in فَاعِلٌ with those radicals to obtain نَاصِرٌ.
ضَرَبَ has ḍād, rāʾ, bāʾ and produces ضَارِبٌ.
سَمِعَ has sīn, mīm, ʿayn and produces سَامِعٌ.
The semantic root stays intact; the alif and vowel pattern create the active-participle form.
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Root letters versus the pattern
Active Participles: Definition, Patterns, Paradigms and Derivation
The root of نَصَرَ consists of nūn, ṣād, rāʾ. Replace the three placeholders in فَاعِلٌ with those radicals to obtain نَاصِرٌ.
ضَرَبَ has ḍād, rāʾ, bāʾ and produces ضَارِبٌ.
سَمِعَ has sīn, mīm, ʿayn and produces سَامِعٌ.
The semantic root stays intact; the alif and vowel pattern create the active-participle form.