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Proof root 3 irrational??? N plzzz …

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Proof root 3 irrational??? N plzzz explain it to me clearly with all steps and appropriate explanation?????

Posted by Sankalp Awasthi 7 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Supriya Tiwari 7 years, 4 months ago

Let us assume that √3 is rational So we can write √3 =a/b where b is not equal to 0 and a and b are co primes On squaring both sides we get 3 =a^2 /b^2 a^2=3b^2 (i) a^2 is divisible by 3 so a is divisible by 3 So we can write a= 3c for any integer c a^2 =9c^2 (ii ) From i and ii we get 3b^2 = 9c^2 b^2= 3c^2 b^ 2 is divisible by 3 so b is divisible by 3 Therefore a and b have atleast 3 as a common factor but this contradicts the fact that a and b have no common factor other than 1 This contradiction has arisen because of our wrong assumption that √3 is rational So we conclude that √3 is irrational.

5Thank You

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