Components
極める is an exact match with one form of the following word:
窮める
BOOST
Reading : きわめる   
ichidan verb, transitive verb
1. to carry to extremes; to go to the end of something  (esp. 極める, 窮める)
2. to investigate thoroughly; to master  (esp. 究める)
My mastery:
My current mastery of 窮める:
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Usefulness and usage:
Kanshudo usefulness level: 5 (among the 10,000 most useful words in Japanese)
• Kanshudo usefulness level is based on a usefulness score of 86,564 which gives a rank of 7,798
窮める is the most useful form. 3 additional forms are shown below.
• This form is rarely used
• Google Japan frequency rank: 246,000 (about 19,300 results)
• This form is used as an example of an official Joyo kanji reading
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Example sentences:
かれ
たぼう
多忙
きわ
めていた
ので
じぶん
自分
かないで
むすこ
息子
かせた

He was so busy that he sent his son instead of going himself.
おお
うんどう
運動
せんしゅ
選手
せいねん
青年
じだい
時代
きわ
める

Most athletes are at their best during their early manhood.
この
にんむ
任務
かんりょう
完了
する
こんなん
困難
きわ
めた
こと
うまでもない

It goes without saying that it was supremely difficult to carry out this mission.
Useful expressions:
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究める
BOOST
Reading : きわめる   
My flashcards:
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Usefulness and usage:
• This form is used about 10% of the time
• Google Japan frequency rank: 111,000 (about 1,380,000 results)
• This form is used as an example of an official Joyo kanji reading
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極める
BOOST
Reading : きわめる   
My flashcards:
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Usefulness and usage:
• This form is used about 80% of the time
• Google Japan frequency rank: 54,000 (about 8,000,000 results)
• This form appears in the 1998 'Ichimango goi bunruishuu' frequent word list by Senmon Kyouiku
• This form appears in the 24,000 words in the Mainichi Shimbun frequency analysis by Alexandre Girardi
• This form is in band 30 in the EDICT word frequency file (bands go from 1-48, where 1 is most common - each contains about 500 words)
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きわめる
BOOST
My flashcards:
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Usefulness and usage:
• This form is rarely used
• Google Japan frequency rank: 188,000 (about 353,000 results)
• This form appears in the 1998 'Ichimango goi bunruishuu' frequent word list by Senmon Kyouiku
• This form appears in the 24,000 words in the Mainichi Shimbun frequency analysis by Alexandre Girardi
• This form is in band 30 in the EDICT word frequency file (bands go from 1-48, where 1 is most common - each contains about 500 words)
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キュウ   きわめる to investigate thoroughly   
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ク   キュウ   ここの nine   
ケツ   あな hole   
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katakana 'ha'; eight
roof   
キュウ   きわまる to reach an extreme   きわめる to go to extremes   
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シン   み body, person   
キュウ   ゆみ a bow   
キョク   ゴク    extreme, end, pole   きわめる to carry to its end   きわまる to reach an extreme   きわまり extremity   
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モク   ボク   き    こ- tree   
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ダイ   タイ   おおきい big   おおいに very much   おお-    
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イチ   イツ   ひと    ひと- one   
ジン   ニン   ひと person   
stick   
reach the mouth again
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reach
コウ   ク   くち mouth   
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また again   
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