Classify the following numbers as rational or irrational:
(i) $ \sqrt{23} $
(ii) $ \sqrt{225} $
(iii) $ 0.3796 $
(iv) $ 7.478478 \ldots $
(v) $ 1.101001000100001 \ldots $
To do:
We have to classify the given numbers as rational or irrational.
Solution:
(i) $\sqrt{23}=4.795831523..........$
The decimal expansion of \( \sqrt{23} \) is non-terminating and non-recurring.
Therefore, \( \sqrt{23} \) is an irrational number.
(ii) $\sqrt{225}=15$
The decimal expansion of \( \sqrt{225} \) is terminating.
Therefore, \( \sqrt{225} \) is a rational number.
(iii) \( 0.3796 \)
The number $0.3796$ is terminating.
Therefore, it is a rational number.
(iv) \( 7.478478 \ldots \)
The number $7.478478$ is non-terminating but recurring.
Therefore, it is a rational number.
(v) \( 1.101001000100001 \ldots \)
The number $1.101001000100001…..$ is non-terminating non-repeating (non-recurring).
Therefore, it is an irrational number.
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