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Prove √ 2 is irrational

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Prove √ 2 is irrational

Posted by Anju Gupta 7 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Kannu Kranti Yadav 7 years, 4 months ago

Let , us assume that √2 is rational number then it can be written in the form of a/b where b≠0 and (a,b are co prime numbers). So, √2=a/b, now squaring on both sides gives 2=a²/b²... 2b²=a² so we can say thay a² is divisible by 2 , therefore a is also divisible by 2. Then take a=2c, now putting value ofa and squaring on both sides giv gives us ...... 2b²=4c² => b²=2c² so b² is divisible by 2 therefore b is also divisible by 2. Hence our assumption is wrong , they have other common factor as 2. There fore √2 is irrational.hence, proved

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CBSE > Class 10 > Mathematics