Question

prove that root P + root Q is irrational number​

Answer 1

Answer:

=> √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. Rational numbers are closed under multiplication, so if we square both sides, we still get rational numbers on both sides. ... But this is a contradiction.

Answer 2

Step-by-step explanation:

Let √p + √q = a, where a is rational. => √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. Rational numbers are closed under multiplication, so if we square both sides, we still get rational numbers on both sides

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