Prove that 1/3+√3 is irrational
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sum of rational and an irrational number is is always irrational
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Let us assume that 1/3+sqrt3 is a rational number.
=> 1/3+sqrt 3=a where 'a' is a rational number
=> sqrt3= a-1/3
Here 'a' is a rational number and we know that 1/3 is also a rational number.
=> a-1/3 is also a rational number.
=> sqrt3 is a rational number.
But it contradicts the fact that root 3 is an irrational number.
Thus, our assumption is wrong.
Therefore 1/3+sqrt3 is an irrational number.
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