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Question

Select the correct option about the numbers given below.

(i) √27

(ii) √256

(iii) 0.3796

(iv) 7.478478...

(v) 1.101001000100001...


A

(i) and (v) are irrational

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B

(iv) and (v) is irrational

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C

only (v) is irrational

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D

none are irrational

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Solution

The correct option is A

(i) and (v) are irrational


(i) The decimal expansion of √27 is non-terminating non-recurring, therefore it is an irrational number.

(ii) √256 =16. This is a rational number as it can be represented in pq form (q is not zero ).

(iii) 0.3796 is terminating decimal expansion , therefore, it is a rational number.

(iv) 7.478478…. This decimal expansion is non-terminating recurring, therefore, it is a rational number.

(v) 1.101001000100001…is non-terminating non-repeating decimal expansion, therefore, it is an irrational number.

So, (i) and (v) are irrational.


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