Question

# If p, q are prime positive integers, prove that √p+√q is an irrational number.

Solution

## Let √p+√q is rational number A rational number can be written in the form of a/b ( where a and b are co-prime ie they have no common factor other than 1.) √p+√q=a/b √p=a/b-√q √p=(a-b√q)/b p, q are integers and we supposed that √q is rational then (a-b√q) /b is a rational number. So, √p is also a rational number.  But this contradicts the fact that √p is an irrational number.  so, our supposition is false √p+√q is an irrational numberMathematicsRD SharmaStandard X

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