根強(ねづよ)いfirmly rooted, deep-seated

今(いま)はＫ(ケー)-ＰＯＰ(ポップ)が根強(ねづよ)い人気(にんき)を誇(ほこ)っています。

KPOP currently boasts a deep-seated popularity.

根強(ねづよ)く残(のこ)っている迷信(めいしん)を消(け)し去(さ)るのは困難(こんなん)である。

It is difficult to dispel superstitions that are firmly rooted.

根強(ねづよ)い努力(どりょく)を重(かさ)ね、ようやく志望(しぼう)大学(だいがく)に入学(にゅうがく)しました。

After persistent efforts, I finally enrolled in my desired university.

監督(かんとく)：「お前(まえ)が一(いち)位(い)になれたのは根強(ねづよ)い頑張(がんば)りを重(かさ)ねたからだぞ。」

Director: 'The reason you were able to become number one is because of your tenacious perseverance.'

寝込(ねこ)みを襲(おそ)って結婚(けっこん)するという今(いま)も根強(ねづよ)く残(のこ)るその国(くに)の習慣(しゅうかん)は消(き)えるべきだ。

The custom in that country that is still firmly rooted, where you marry someone by attacking them in their sleep, should be eradicated.