# sum, product of rational and irrational number

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.