Answer: Option (b) is the correct answer.
Step-by-step explanation:
A number which cannot be expressed in the form of [tex]\frac{p}{q}[/tex] is known as irrational number. An irrational number are non-terminating and non-repeating numbers.
For example, 0.5, square root of 2 etc are irrational numbers.
Sum of a rational number and irrational number always produces an irrational number. Therefore, 0.5 which can also be written as [tex]\frac{1}{2}[/tex] when added to square root of 3 will produce an irrational number.
Whereas 0.555... is non-terminating and repeating. Hence, it is not an irrational number.
Similarly, [tex]\frac{1}{3}[/tex] and square root of 16 are rational numbers.
Thus, we can conclude that out of the given options, square root of 3 produces an irrational number when added to 0.5.
