Question

Prove that 5√3 is irrational

Answer 1

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Answer 2

Assume 5√3 to be Rational .....
therefore it can be written in the form A/B right??
So 5√3=a/b .........
√3=a/5b.......
here a /b is rational also dividing it by 5 it still stays rational that means rhs is rational but look carefully lhs is irrational.....
therefore our contradiction is wrong 5√3 is irrational......
also by logic rational * irrational will be irrational......
there is no logic to prove that