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
• B. (iv) and (v) is irrational
• C. only (v) is irrational
• D. none are irrational

Answer 1

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 $\frac{p}{q}$ 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.