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]
