根本无法：完全不可能 (-ㄹ/을 수가 없다)

1. 1Verb Stem: This is the base form of an action verb, derived by removing 다 (da) from its dictionary form (e.g., 가다 (ga-da) → 가 (ga); 먹다 (meok-da) → 먹 (meok)). This pattern is predominantly used with action verbs as it describes the impossibility of performing an action.

1. 1(-ㄹ/을) (Prospective Adnominal Ending): This ending transforms the verb stem into a form that modifies a noun, indicating potential, future action, or a hypothetical situation. It translates roughly to that will or to be (doing). The choice between -ㄹ and -을 depends on the verb stem's final sound:

• If the verb stem ends in a vowel or the consonant ㄹ, use -ㄹ (e.g., 가 + ㄹ → 갈; 만들 + ㄹ → 만들).
• If the verb stem ends in any other consonant, use -을 (e.g., 먹 + 을 → 먹을; 읽 + 을 → 읽을).

1. 1수 (Dependent Noun): The Korean word 수 (數, su) functions here as a dependent noun. In this context, it signifies a way, a method, a means, or a possibility. Crucially, as a dependent noun, 수 cannot stand alone and must be preceded by a modifying clause (in this case, the verb stem with the adnominal ending (-ㄹ/을)). Therefore, (-ㄹ/을 수) translates to

   a way to [verb]

   or

   the possibility of [verb]-ing.

1. 1가 (Subject Particle): This is where (-ㄹ/을 수가 없다) gains its distinctive emphasis. The particle 가 (ga) marks 수 (su) as the grammatical subject of the sentence. By explicitly making the way/possibility the subject, the sentence foregrounds the *absence* of this very way or possibility. It's like saying,

   *As for* the way to [verb], it does not exist.

   This structural choice underscores that the impossibility is not just about one's personal inability, but about the fundamental non-existence of a path for the action to occur, often implying external factors or an overwhelming state.

1. 1없다 (Negative Adjective): The final component, 없다 (eopda), is an adjective meaning to not exist, to not be, or to not have. It is the core negative element of the entire construction. Since 없다 is an adjective, it is conjugated for tense and formality, not the preceding verb.

No, 가 is not grammatically mandatory, but its presence significantly changes the nuance and emphasis. The pattern (-ㄹ/을 수 없다) without 가 means a neutral cannot or is unable to. It's a factual statement of inability.

• 지금 갈 수 없어. (Ji-geum gal su eop-seo.) - "I can't go right now." (Neutral, factual.)
• 지금 갈 수가 없어. (Ji-geum gal su-ga eop-seo.) - "There's no way I can possibly go right now." (Emphatic, conveying a strong barrier or frustration.)

Yes, (-ㄹ/을 수가 있다) (romanized: (-l/eul su-ga it-da)) is grammatically correct and means

it is certainly possible

there is definitely a way.

• 그가 해낼 수가 있을 거예요. (Geu-ga hae-nael su-ga it-sseul geo-ye-yo.) -

  He will definitely be able to do it.

• 새로운 기술을 개발할 수가 있어요. (Sae-ro-un gi-sul-eul gae-bal-hal su-ga it-sseo-yo.) -

  It is certainly possible to develop new technology.

The pattern itself is neither inherently formal nor informal; its level of politeness or formality is determined by how the final verb 없다 is conjugated. You can use this pattern across all speech levels:

• Formal (합니다체): 갈 수가 없습니다 (gal su-ga eop-seup-ni-da)
• Polite Casual (해요체): 갈 수가 없어요 (gal su-ga eop-seo-yo)
• Casual (해체): 갈 수가 없어 (gal su-ga eop-seo)

No, (-ㄹ/을 수가 없다) is primarily used with action verbs. Adjectives describe states, qualities, or conditions (예쁘다 'to be pretty', 크다 'to be big'), not actions that can have a way or method. Applying this pattern directly to adjectives results in grammatically awkward or incorrect sentences. To express the impossibility of a state or to strongly deny that something is a certain way, you would typically use (-ㄹ 리가 없다).

• Incorrect: 이것이 예쁠 수가 없어요.
• Correct (for denying a state): 이것이 예쁠 리가 없어요. (I-geot-i ye-ppeul ri-ga eop-seo-yo.) - "There's no way this is pretty."

The dramatic pause after 수 or 수 가 in media like K-dramas is a rhetorical device used to heighten the emotional impact and emphasize the profound nature of the impossibility or disbelief. By pausing, the speaker draws attention to the 수 (the way or possibility) that is being negated, making the audience feel the weight of its absence.

Yes, it can be used in formal contexts like a job interview, but with caution and politeness. When used to explain a genuine, unavoidable constraint or inability, it can convey professionalism and clarity. For instance, if asked about a task that is genuinely impossible given current resources, you might respond:

• 현재 인력으로는 이 프로젝트를 기한 내에 완료할 수가 없습니다. (Hyeon-jae il-lyeok-eu-ro-neun i peu-ro-jek-teu-reul gi-han nae-e wan-ryo-hal su-ga eop-seup-ni-da.) - "With the current personnel, there's no way we can complete this project within the deadline."