Final answer:
Any irrational number, such as the square root of 2, when multiplied by 1/2, will result in another irrational number. Furthermore, non-terminating, non-repeating decimals are also examples of irrational numbers.
Step-by-step explanation:
The question asks which number, when multiplied by 1/2 (one-half), produces an irrational number. An irrational number is a number that cannot be expressed as a ratio of two integers.
Since multiplying by 1/2 is equivalent to dividing by 2, to obtain an irrational number we need to start with a number that is already irrational.
For example, the square root of 2 (√2) is irrational. When you multiply √2 by 1/2, the result is √2/2, which is also irrational.
Therefore, any irrational number multiplied by 1/2 will still be irrational.
Additionally, any non-terminating, non-repeating decimal or a number that is a result of an undefined operation can also be considered irrational.