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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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