0.5 is a rational number. To keep the sum rational, the addend must also be rational. The square root of a number which is not itself a perfect square is irrational, so A cannot be the answer, because the sum would be irrational. B is a rational number and therefore when added to 0.5 produces another rational number, 0.75.
C and D are rational if the decimals are terminated as shown. Irrational numbers have non-terminating decimals. However D looks like -√3 to 8 places of decimals and C may be another irrational number accurate to 8 decimal places.
The most likely answer is B.
[If the question had been: which number produces an irrational number when added to 0.5, the answer would have certainly been A.]