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Sum-product of rational and irrational number

Question:

Sum, product of rational and irrational number

1. Prove or disprove each of the following:

a. The sum of a rational number and an irrational number is an irrational number.

b. The product of two rational numbers is a rational number.

c. The product of two irrational numbers is an irrational number.

d. The product of a rational number and an irrational number is an irrational number.

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Algebra: Sum-product of rational and irrational number

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