Śrīmad-Bhāgavatam 4.16.15
రఞ్జయిష్యతి యల్లోకమయమాత్మవిచేష్టితై:
అథాముమాహూ రాజానం మనోరఞ్జనకై: ప్రజా: ॥ ౧౫ ॥
raṣjayiṣyati yal lokam
[rashjayishyati yal lokam]
ayam ātma-viceṣṭitaiḥ
[ayam aatma-vicheshtitaih]
athāmum āhū rājānaṁ
[athaamum aahoo raajaanam]
mano-raṣjanakaiḥ prajāḥ
[mano-rashjanakaih prajaah]
Word-for-word
raṣjayiṣyati
—
will please
yat
—
because
lokam
—
the entire world
ayam
—
this King
ātma
—
personal
viceṣṭitaiḥ
—
by activities
atha
—
therefore
amum
—
him
āhuḥ
—
they call
rājānam
—
the King
manaḥ-raṣjanakaiḥ
—
very pleasing to the mind
prajāḥ
—
the citizens.
Blended reading (Sanskrit + English inline)
raṣjayiṣyati yal lokam
raṣjayiṣyati
will please
yat
because
lokam
the entire world
ayam ātma-viceṣṭitaiḥ
ayam
this King
ātma
personal
viceṣṭitaiḥ
by activities
athāmum āhū rājānaṁ
atha
therefore
amum
him
āhuḥ
they call
rājānam
the King
mano-raṣjanakaiḥ prajāḥ
manaḥ-raṣjanakaiḥ
very pleasing to the mind
prajāḥ
the citizens.
This King will please everyone by his practical activities, and all of his citizens will remain very satisfied. Because of this the citizens will take great satisfaction in accepting him as their ruling king.
Gauḍīya Ācāryas
Viśvanātha Cakravartī Ṭhākura
Gauḍīya
Translation
Because he will please (raṣjayiṣyati) the world by his activities which are pleasing to the mind, the citizens will call him the King (rāja).
Because the world will be pleased by his acts which give happiness to the mind (manaḥ raṣjanakaiḥ), they will call him “king.” Rāja is derived in two ways. Some say rāja comes from rājati (he shines). Here it is said that rāja comes from raṣjayati (he attracts or pleases).
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Source: vedabase.io