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Prove 1 upon root 2 is …

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Prove 1 upon root 2 is irrational number

Posted by Amit Singh 1 year, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Aashika Bi 1 year, 7 months ago

Let 1/√2 be a rational number So 1/√2= p/q where p and q are co primes and q≠0 q/√2=p Squaring on both sides, q²/2=p² —(1) Here, q² is divisible by 2 so q is also divisible by 2 Let q=k Put value of q in equation (1) k²/2=p² Divide by 2 on both sides k²/4=p²/2 Here, p² is divisible by 2 so p is also divisible by 2 But we have assumed that p and q are co primes This contradiction has arisen due to our wrong assumption Hence 1/√2 is an irrational number

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