Classify the following numbers as rational or irrational :
(i) \(\sqrt23 \)
(ii) \(\sqrt225 \)
(iii) 0.3796
(iv) 7.478478...
(v) 1.101001000100001...
Classify the following numbers as rational or irrational :
(i) \(\sqrt23 \)
(ii) \(\sqrt225 \)
(iii) 0.3796
(iv) 7.478478...
(v) 1.101001000100001...
Solution and Explanation
(i) \(\sqrt23\) = 4.79583152331.... As the decimal expansion of this number is non-terminating non-recurring, therefore, it is an irrational number.
(ii) \(\sqrt225\) = 15= \(\frac{15}{1}\)It is a rational number as it can be represented in \(\frac{p}{q}\) form.
(iii) 0.3796 As the decimal expansion of this number is terminating, therefore, it is a rational number.
(iv) 7.478478 … = \(\overline{7.478 }\) As the decimal expansion of this number is non-terminating recurring, therefore, it is a rational number.
(v) 1.10100100010000 … As the decimal expansion of this number is non-terminating non-repeating, therefore, it is an irrational number.
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