Which of the following is irrational? (refer to attached image)

Answer:Option C is irrational number that is [tex]\sqrt{3} + 8.486[/tex]Step-by-step explanation:Irrational numbers have:Non-repeating and non-terminating decimals.Numbers that can't be expressed as [tex]\frac{a}{b}[/tex] ratios.Lets look at [tex]7.5\bar{1} .(-4)[/tex] ,which is having [tex]\bar{1}[/tex]  being repeated so it fails the irrational test.Now we have [tex]\sqrt{16} = 4[/tex] so it fails the irrational test.The last one is [tex]8\tfrac{2}{3} =\frac{26}{3} =8.666666667[/tex] here we can write the decimal as [tex]\bar{6}[/tex] which is repeating in itself so it also fails irrational test.Then[tex]\sqrt{3} =1.73205[/tex] is non-repeating and non-terminating so we can say that it it is added with [tex]8.486[/tex] is doesn't effect more and the whole [tex]\sqrt{3} +8.486[/tex] is an irrational number.So the  irrational number is [tex]\sqrt{3} + 8.486[/tex]