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Prove that 1\√2is irrational

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Prove that 1\√2is irrational

Posted by Prakash Vyas 5 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

? Pranali.A.P ? 5 years, 4 months ago

To prove 1/√2 is irrational............. Let us assume that √2 is irrational .......... 1/√2 = p/q (where p and q are co prime)........ q/p = √2......... q = √2p....... squaring both sides......... q² = 2p² .....................(1) By theorem ...... q is divisible by 2....... ∴ q = 2c ( where c is an integer)....... putting the value of q in equitation 1....... 2p² = q² = 2c² =4c² ...... p² =4c² /2 = 2c²..... p²/2 = c² ..... by theorem p is also divisible by 2..... But p and q are coprime........ This is a contradiction which has arisen due to our wrong assumption.... ∴1/√2 is irrational

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