Question

The multiplication of two irrational numbers may result in a/an

• A. Irrational number
• B. Rational number
• C. Real number
• D. All of the above

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A

Irrational number

B

Rational number

C

Real number

D

All of the above

The multiplication of two irrational numbers may result either in a rational or an irrational number.

Consider the following example: $(\sqrt{3}+\sqrt{2})\times (\sqrt{3}-\sqrt{2})=1$.
Both $(\sqrt{3}+\sqrt{2})$ and $(\sqrt{3}-\sqrt{2})$ are irrational numbers and their multiplication results in 1.
1 is an integer and since all integers are rational numbers as well (and hence real numbers), we can infer that multiplication of two irrational numbers may result in an integer, a rational number or a real number.

When we multiply the irrational numbers $\sqrt{2}$ and $\sqrt{3}$, we get $\sqrt{6}$, which is also an irrational number.