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sum, product of rational and irrational number

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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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Solution Preview

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.
a. Here ...

Solution Summary

To conclude what happens after certain operation (summation, multiplication) between rational and irrational numbers, it is important to remember that 0 is one of the rational numbers that can either disprove or prove some proposition.

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