If x x x is a rational number and y y y is an irrational number, then which of the following statements is true?

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Question

x

is a rational number and

y

is an irrational number, then which of the following statements is true?

both x + y and xy are necessarily rational

both x + y and xy are necessarily irrational

xy is necessarily irrational, but x + y can be either rational or irrational

x + y is necessarily irrational, but xy can be either rational or irrational

arithmetic operationsrational numbersirrational numbers

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