Question

prove that √3 is an irrational number in brainly.




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Answer 1

let √3 be rational no.

so,

√3 = p / q ( where p , q are co - prime and q is not equal to 0)

squaring on both sides

3 =p^2 /q^2

3 q^2 = p ^2 --------- (1)equation

therefore p^2 is divisible by 3

so, p is also divisible by 3

by (1) equation

3 q^2= (3r) ^2 [ where r is belongs to any integer ]

3 q ^2 = 9r^2

q^2= 3r^2

therefore q^2 is divisible by 3

so, q is also divisible by 3 ----------(2) equation

by (1) and (2) equation p and q have 3 as common factor. But this is contradicts the fact they p and q are co prime which have no common factor than one.

=>our supposition is wrong ..

hence√3 is a irrational no.

hope it helps