prove that root 2 is irrational
Risabh kumar , 9 Years ago
Grade 10
10 grade maths> prove that root 2 is irrational
1 AnswersRakshita S Kumtakar
Last Activity: 9 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=2C2 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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