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

Which of the following is irrational? (refer to attached image)-example-1

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6 votes

Answer:

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

User Nolik
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