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CBSE Class 10 Answered

Prove that  6 square root of 2 an irrational number
Asked by swaritlall | 15 Apr, 2020, 07:36: AM
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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