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Prove that √2 is irrational

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Prove that √2 is irrational

Posted by Beauty Queen Miss Sweetu ? 6 years, 11 months ago

CBSE > Class 10 > Social Science

1 answers

Archana Pandit 6 years, 11 months ago

Let,root two is rational such that Root two=a/b Now square ing on both sides Then Two=a square/b square Two×b square=a square.......(1) Here Two is factor of a sq So Two is also factor of a Let,a=2r for some integer Putting the value in eq-1 Two×b sq=(2r)sq =2×b sq =4r sq So,b sq=2 r sq Clearly 2is also a factor of b Hence,2 is a common factor of a &b It is a contradiction that arises by assuming root as rational So,root two is irrational

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CBSE > Class 10 > Social Science