Question

prove that root q+root p is an irrigation number

Answer 1

let √p+√q is rational
then it can be written in form a/b
√p+√q=a/b
√p =a/b-√q
squaring both sides
p=(a/b-√q)whole square
p=asquare/b square +q-2a/b×√q
p-a square / b square +q=2 a/b×√q
we know that here the left hand side is a whole number whereas right hand side is an irrational no.
hence a rational can never be equal to an irrational no.
thus,√p+√q is irrational

Answer 2

Answer:

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