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Prove that root 3 is irrational …

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Prove that root 3 is irrational number

Posted by Abhishek Bandane 7 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Achal Bharadwaj 7 years, 1 month ago

Let us assume that √3 is a rational number a and b are coprime number a/b =√3 a square /b square = 3 b square =a square /3. ---------------- (1) 3 divides a square , 3div a also a = 3c ------------------------- (2) Substitute (2) in (1) b square = (3c) square / 3 =9c square /3 = 3c square c square = b square /3. ---------------(3) 3div a square , 3div a also From (1) (2) (3) There is a contradiction to our assumption that a and b are coprime number Therefore √3 is an irrational number HENCE PROVED ✓

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