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Prove that  6 square root of 2 an irrational number
Asked by swaritlall | 15 Apr, 2020, 07:36: AM
answered-by-expert Expert Answer
begin mathsize 18px style let space 6 square root of 2 space be space rational 6 square root of 2 equals straight p over straight q.... straight p space and space straight q space are space co space prime squaring 72 straight q squared equals straight p squared...... open parentheses 1 close parentheses 72 space divides space straight p squared so 72 space divides space straight p straight p equals 72 straight c... sub space in space open parentheses 1 close parentheses 72 straight q squared equals 72 squared straight c squared straight q squared equals 72 straight c squared 72 space divides space straight q squared so 72 space divides space straight q so space 72 space divides space straight p space and space straight q space both comma space which space is space not space possible space since space they space are space co space prime hence space assumption space is space wrong 6 square root of 2 space is space not space rational end style
Answered by Arun | 15 Apr, 2020, 09:53: AM

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