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in Number System by (58.8k points)

Classify the following numbers as rational or irrational:

(i) 2.040040004....

(ii) 1.535335333.....

(iii) 3.121221222...

(iv) \(\sqrt{21}\)

(v) \(3\sqrt3\)

1 Answer

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Best answer

(i) 2.040040004…

An irrational number. It is a non-terminating and non-repeating decimal.

(ii) 1.535335333…

An irrational number. A non-terminating and non-repeating decimal.

(iii) 3.121221222…

An irrational number. A non-terminating and non-repeating decimal.

(iv) \(\sqrt{21}\)

An irrational number.

21 = 3 × 7 is an irrational number. And 3 and 7 are prime and irrational numbers.

(v) \(3\sqrt3\)

An irrational number.

3 is a prime number. So, 3 is an irrational number.

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