Prompt Title: Korean title: 한국어로 번역해주세요 (Please translate into Korean)

The word "indispensable" can be translated into Korean as "필수적인" (pilsujeog-in).

The word "bilateral" can be translated into Korean as "양측의" (yangcheok-ui).

"The main example was bilateral or mirror-image symmetry" can be translated into Korean as "주요한 예시는 양측 대칭 또는 거울 대칭이었다" (juyohan yesineun yangcheok daesyeong ttoneun geoul daesyeongieossda).

"The fivefold symmetry" can be translated into Korean as "5배 대칭" (obbae daesyeong) or "5중 대칭" (objung daesyeong).

"Mathematicians and scientists would have a solid base" can be translated into Korean as "수학자와 과학자들은 견고한 기반을 갖게 될 것이다" (suhakja wa gwahakjadeureun gyeongohan gibaneul gajge doel geosida).

The word "radicals" can have different translations in Korean depending on the context. Here are some possibilities:

• In mathematics, "radicals" as in "square root" or "cube root" can be translated as "근 (geun)" or "루트 (ruteu)".
• In chemistry, "radicals" can be translated as "라디칼 (radikal)".
• In politics or social contexts, "radicals" can be translated as "급진주의자 (geupjinjuuija)" or "극단주의자 (geukdanjuuija)".
• In general, "radicals" can be translated as "근본적인 (geunbonjeog-in)" or "극단적인 (geukdanjeog-in)" depending on the meaning intended.

"A group of permutations" can be translated into Korean as "순열의 군 (sunyeol-ui gun)" or "순열 군 (sunyeol gun)".

"Awe-inspiring" can be translated into Korean as "경외감을 불러 일으키는" (gyeongoe gam-eul bulleo il-eukineun) or "존경심을 일으키는" (jongyeongsim-eul il-eukineun).