Which number produces a irrational number when added to 0.5?
0.555
1/3
square root of 16
square root of 3
The numbers that produce an irrational number when added to 0.5 are:
- 0.555
- Square root of 3
To determine which number produces an irrational number when added to 0.5, we can check whether the resulting sum is rational or irrational.
1. 0.555 + 0.5 = 1.055. This sum is a rational number since it can be expressed as a fraction (211/200).
2. 1/3 + 0.5 = 0.8333... The sum is a rational number since it repeats and thus can be expressed as a fraction (5/6).
3. √16 + 0.5 = 4 + 0.5 = 4.5. This is a rational number since it can be expressed as a fraction (9/2).
4. √3 + 0.5 ≈ 1.732 + 0.5 = 2.232. This sum is an irrational number since it cannot be expressed as a fraction and has a non-repeating decimal expansion.
Therefore, the number that produces an irrational sum when added to 0.5 is the square root of 3.