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to prove root 2is irrational

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to prove root 2is irrational

Posted by Mandeep Singh 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Amna Nasim 6 years, 11 months ago

let us assume that root 2 is rational no. which is in the form of p/q , where q is not equal to 0. therefore, root 2 = p/q squaring both the sides 2 = p^2/q^2 2q^2 = p^2 ....(1) Here, 2 is divisible by p^2 therefore, 2 is also divisible by p let p = 2c [for some integer c] now, substituting p = 2c in equation (1). therefore, 2q^2 = 4c^2 that is q^2 = 2c^2 this means that 2 is divisible q^2 and so 2 is also divisible by q since p and q have 2 as a common factor this contradict the fact that p & q have no common factor other than 1. But this contradiction has arisen due to our wrong assumption that is root 2 is rational no. so, we conclude that root 2 is irrational.

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CBSE > Class 10 > Mathematics