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Prove that 1/2 is irrational

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Prove that 1/2 is irrational

Posted by Vivek Yadav 5 years, 5 months ago

CBSE > Class 10 > Mathematics

3 answers

Vivek Yadav 5 years, 5 months ago

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Ayush Raj 5 years, 5 months ago

1/2 is not an irrational number

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Nikku Shekhawat 5 years, 5 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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Posted by Kanika . 1 week ago

CBSE > Class 10 > Mathematics

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Posted by Hari Anand 5 months, 1 week ago

CBSE > Class 10 > Mathematics