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prove that root 2 is irrational

prove that root 2 is irrational 
 

Grade:10

1 Answers

Rakshita S Kumtakar
25 Points
6 years ago
LET US ASSUME THAT ROOT2 IS RATIONAL.
SO, ROOT2 CAN BE EXPRESSED AS P/Q
SUPPOSE P AND Q HAVE A COMMON FACTOR , V CAN DIVIDE THEM BY A COMMON FACTOR AND GET
ROOT2=A/B WHERE A AND B ARE COPRIME.
SO  B(ROOT2)=A
SQUARING BOTH THE SIDES,
WE GET 2B2=A2
SO,2 DIVIDES A2
SO, 2 DIVIDES A ALSO.
 V CAN WRITE A=2C  FOR SOME INTEGER C
SUBSTITUTING A,WE GET ROOT2=2C
SQUARING BOTH SIDES, 2B2=4C2
B2=2C SO 2 DIVIDES B
A AND B HAVE 2 AS COMMON FACTOR.BUT THIS CONTRADICTS THE FACT THAT A AND B HAV NO COMMON FACTOR OTHER THAN 1.SO UR ASSUMPTION THAT ROOT 2 IS WRONG.
THEREFORE ROOT 2 IS IRRATIONAL.
 

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