いか

いか

いか is an old, more formal variant of どう/どんな (how).
いか(が) is sometimes written as 如何 (Same as the kanji for どう)
いか almost never appears by itself, instead appearing in conjunction with a particle.
This page covers:

  • いかが – How (Noun)
  • いかなる – How (adjective) 
  • いかに – How (adverb)
  • いかにも – Certainly/very

See also いかん, a related term too large to cover here. 

いかが

Noun
How is it?
どう?

いかが is the noun version of いか. Used exactly like どう.
Almost exclusively used as:
XXXは+ いかが + ですか/でしょうか

Examples

  • いかがでしょうか
    How is it? (Very polite)

  • ほかに何かいかがですか (Weblio)
    How about something else?

  • この提案はいかがかと思う (Weblio)
    I don’t know (how) about that proposal. (どうかと思う is an expression expressing doubt). 

いかなる

Adjective
However it is
どんな

いかなる is the adjective version of いか/どう.
Its meaning is essentially どんな
Literally it means something like “However (it is)”

Examples

  • いかなる時に備える
    Prepare for any kind of time. (However the time is).

  • いかなる形でも関わりたい
    I want to be involved no matter the form.

  • いかなる手段を使っても阻止したい
    I want to stop it no matter the kind of methods I have to use.

  • いかなる反対を無視する
    Ignore any kind of disagreement.

いかに

Adverb
How…(did you, much, come)
どのように、どんなに、どうして

いかに is the adverbial version of いか.
It can be used like the adverbial version of どう. 
It is used to express:

  1. How (some state) – どのよう
  2. How much – どんな・どれほど
  3. How come – どうして (Rare) Included because of いかにも meaning (see below)

Examples

  • 人間、いかに生くべきか (Weblio)
    Humans, how should they live. 

  • 彼女はいかに泣いたことか
    (Do you know) how much she cried. (How she cried).

  • いかに頑張っても限界がある
    No matter how much you try there is a limit.

いかにも

That’s Definitely/Very
実に、確かに、どうしても

いかにも is also an adverbial version of いか, but is used to express that something is “definitely” or “truly”. 
It can be used to express:

  • Certainly/Truly – 実に、確かに - Used a lot with らしい, そう, and よう
  • Seeming very – とても + そう Basically a consequence of the above. Limited to appearances. 
  • Via any method – どうして (rare)

Examples

  • いかにも彼らしい
    That’s definitely like him.

  • いかにも悲しそうに手を振った
    He very sad seeming waved his hand (goodbye). 

  • いかにも(そうだ)
    Certainly/That’s definitely the case. (Expression used to indicate strong agreement).

  • いかにもこけそうだ
    It really looks like they are about to fall.

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