Question

p t √5 is a irrational number​

Answer 1

Answer:

let root 5 be rational

there for √3=a/b.(a and b are integer and not equal to 0)

suppose a and b have have common factor other than 1,then we can divide by the common factor, and asume that a and bare coprime.

so, b√3=a.

on squaring both side we get,

3b^2=a^2.

thereforea^2is divisible by 3and b is also divisible by 3

therefore a and b have at least 3 as common factor.

But this contradicts the fact a and b are coprime.

This contradiction arises due to our wrong assumption.

Therefore√3 is irritional.

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