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Prove 2is rational no.

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Prove 2is rational no.

Posted by Niraj Singh 7 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Kannu Kranti Yadav 7 years, 1 month ago

Let , √2 be a rational number . Then it can be written in the form of a/b where b≠0 and ( a,b are co prime no.s) √2=a/b , now squaring on both sides.. 2= a²/b²... 2b²=a² .. it means a² is divisible by 2 . So a is also divisible by 2. .......... Let , a=2c , now squaring on both sides a²=4 c² putting value of a²... 2b²=4c² --> b²=2c² it means b² is divisible by 2 , so b is also divisible by 2 . Therefore our assumption is wrong . Hence, due to contradiction √2 is an irrational number as it has other common factor other than a and b . Hence, proved that √2 is an irrational number

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