Question

prove that √p+√q is irrational , where p and q are primes.​

Answer 1

Let √p+√q is rational number

A rational number can be written in the form of a/b

√p+√q=a/b

√p=a/b-√q

√p=(a-b√q)/b

p, q are integers 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 number

Answer 2

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