Question

Which number produces an irrational number when added to 0.4

Answer 1

To produce an irrational number when added to 0.4, any number that is not rational can be used.

Step-by-step explanation:

In order to find a number that produces an irrational number when added to 0.4, we need to understand what makes a number irrational. An irrational number is a number that cannot be expressed as a fraction, and it has an infinite number of non-repeating decimal digits.

If we add a rational number to 0.4, the result will always be a rational number. For example, if we add 0.3 to 0.4, the result is 0.7 which is a rational number.

Therefore, any number that is not rational will produce an irrational number when added to 0.4. For example, √2 or π can be added to 0.4 to obtain irrational sums.

Answer 2

Any other irrational number. 0.4 is rational (ie., it can be written as a fraction), but rational+irrational is always irrational.

So examples would be π or √2. If you add those, the result is irrational.