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восхвалять v stresses
gen.	celebrate one's praises; commend; cry up; fuff; puff; record; set forth; set off; sing; vant; chant the praises; aggrandize; be loud in one's praises; belaud; eulogize; exalt; extol; glamorize; glorify; incense; magnify; panegyrize; preach up; rhapsodize (что-либо); throw bouquets; build up; give praise to (кого-либо); sing praises (someone's); lavish praise on (MargeWebley); laud to the skies; praise to the skies; sing the praises of; celebrate (hedgehoglet); aggrandise (Anglophile); vaunt; extoll; glamourize; praise; sing one's praises; trumpet (Alex_Odeychuk); rhapsodize about (Wakeful dormouse); rhapsodise about (Wakeful dormouse); rhapsodize over (Wakeful dormouse); rhapsodise over (Wakeful dormouse)
amer.	hand someone a bouquet for (кого-либо Bobrovska)
austral., slang	lay it on thick
cinema	verse
dipl., amer., fig.	sell
Gruzovik, herald.	blazon
jarg.	kudize
Makarov.	be lavish in someone's praises (кого-либо); be loud in one's praises; lavish praise on (someone – кого-либо); preach up something (что-либо); sing one's praises; sing the praises of (someone – кого-либо)
Makarov., inf.	hand someone a bouquet for (кого-либо); hand bouquets at (someone – кого-либо)
obs.	swell
poetic	chant (в музыкальной форме)
pomp.	be full of praise (of someone/something Andrey Truhachev)
relig.	chant the praises of (кого-либо)
rhetor.	laud
uncom.	superexalt; raise
восхваляться v
gen.	eulogize; extol (be); laud; vaunt
Gruzovik	be eulogized; be extoled; be lauded; be belauded; be vaunted
восхваляя v
gen.	in praise of

восхвалять: 26 phrases in 8 subjects

Business	1
General	13
Informal	1
Makarov	5
Mass media	1
Obsolete / dated	3
Psychiatry	1
Slang	1