Question

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

Answer 1

Option C is irrational number that is
`√(3) + 8.486`

Explanation:

Irrational numbers have:

• Non-repeating and non-terminating decimals.
• Numbers that can't be expressed as
  `(a)/(b)` ratios.

Lets look at
`7.5\bar{1} .(-4)` ,which is having
`\bar{1}` being repeated so it fails the irrational test.

Now we have
`√(16) = 4` so it fails the irrational test.

The last one is
`8\tfrac{2}{3} =(26)/(3) =8.666666667` here we can write the decimal as
`\bar{6}` which is repeating in itself so it also fails irrational test.

Then

`√(3) =1.73205` is non-repeating and non-terminating so we can say that it it is added with
`8.486` is doesn't effect more and the whole
`√(3) +8.486` is an irrational number.

So the irrational number is
`√(3) + 8.486`