Prove that 3 root3 irrational.
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to prove root 3 as irrational....
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..
radhika4471:
Thanksss a lotttttttt
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