Question

The product of any two irrational numbers,
A. is always an irrational number.
B. is always a rational number.
C. is always an integer.
D. can be rational or irrational.

Answer 1

Hint: In order to solve this problem you need to know about irrational numbers. Irrational numbers can’t be expressed as ${\displaystyle \frac{P}{Q}}$ where Q is not equal to 0. Knowing this will solve your problem.

Complete step-by-step answer:
The product of two irrational numbers can be rational or irrational depending on the two numbers.

For example, $\sqrt{3}\times \sqrt{3}$ is 3 which is a rational number whereas $\sqrt{2}\times \sqrt{4}$​ is $\sqrt{8}$​ which is an irrational number. As $\sqrt{3},\sqrt{2},\sqrt{4}$ are irrational.

Hence, option D is correct.

Note: Whenever you face such types of problems you need to know what is a rational number then you can solve this problem. We have done this problem with the thought that after multiplying the number may be an irrational or rational number with the help of an example above. An irrational number is a real number that cannot be expressed as a ratio of two integers. The number π (3.14159...) is a common example of an irrational number since it has an infinite number of digits after the decimal point.