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Prove that root2+1/root2 is irrational number

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Prove that root2+1/root2 is irrational number

Posted by Nikhita Bisht 7 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Somesh Mishra 7 years, 7 months ago

√2+1/√2 =3/√2 =3√2/2 Let us assume that √2+1/√2 is rational. Then there must exist two positive co primes a and b such that √2+1/√2=a/b =>3√2/2=a/b 2a/3b=√2 which is a contradiction. Hence, √2+1/√2 is irrational.

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