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Prove that 5-3/7 root 3 is an irrational number

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Let 5-3/7√3 be rational.Therefore its simplest form will be p/q.Now,5-3/7√3=p/q3/7√3=5-p/q3/7√3=5q-p/q√3= 7(5q-p)/qHere,7,5,p,q are rational numbers.Therefore, √3 will be also a rational no.But this contradicts the fact that √3 is irrational, and this contradiction arises by assuming 5-3/7√3 as rational.Hence 5-3/7√3 is irrational.
No it is no an irrational number


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