Question

prove that root p + root q is irrational

Answer 1

Answer:

see the attachment

Step-by-step explanation:

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Answer 2

Answer:

Let us suppose that √p + √q is rational.  

Let √p + √q = a, where a is rational.  

=> √q = a – √p  

Squaring on both sides, we get  

q = a2 + p - 2a√p

=> √p = (a2 + p - q)/2a, which is a contradiction as the right hand side is rational number, while√p is irrational.  

Hence, √p + √q is irrational.