Question

Prove ​that 3 root3 irrational.

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Answer 1

to prove root 3 as irrational....

$\sqrt{3}$

let root 3 be rational first

so √3=a/b( where A and B are integers b is not equal to zero and A and B are coprime numbers)

( coprime numbers are those numbers which do not have any common factor other than one)

√3=a/b

sq.on both sides

3 =a²/b²

a²=3b²......(¹)

if 3 is the factor of a²then 3 is also the factor of a...

let a=3c

put value of a in 1 equation ..

(3c)²=3b²

9c²=3b²

3c²=b²

so,3 is also the factor of b²and of b.

but A and B are coprime numbers which do not have any number other than one as a common factor but they have three also as a common factor hence there is a contradiction which proves that are assumption was wrong hence if√3is not rational then it is irrational...

hope it may help to dear..