Classify the following numbers as rational or irrational:

(i) √23

(ii) √225

(iii) 0.3196

(iv) 7.478478

(v) 1.101001000100001…
Solution:

(i) $\sqrt{23}=4.79583152331 \ldots$

As the decimal expansion of this number is non-terminating non-recurring, therefore, it is an irrational number.

(ii) $\sqrt{225}=15=\frac{15}{1}$

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) $7.478478 \ldots=7 . \overline{478}$

As the decimal expansion of this number is non-terminating recurring, therefore, it is a rational number.

(v) $1.10100100010000 \ldots$

As the decimal expansion of this number is non-terminating non-repeating, therefore, it is an irrational number.
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