Classify the following numbers as rational or irrational: (i) $$\sqrt{23}$$ (ii) $$\sqrt{225}$$ (iii) $$0.3796$$ (iv) $$7.478478...$$ (v) $$1.101001000100001...$$
Solve the given expressions
(1) $$\sqrt{23}=4.795831523..........$$
The decimal expansion is non terminating non recurring.
$$\therefore \sqrt{23}$$ is a irrational number.
(2)$$ \sqrt{225}=15$$
$$\therefore \sqrt{225}$$ is a rational number.
(3) $$0.3796$$ is the decimal expansion is terminating.
So $$0.3796$$ is a rational number.
(4) $$7.478478......=7.\overline{478}$$ is the decimal expansion is non termination and recurring.
$$7.478478......$$ is a rational number.
(5) $$1.101001000100001......$$ is the decimal expansion is non termination and non recurring. $$71.101001000100001......$$ is a irrational number.
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