Classify the following numbers as rational or irrational: <br/><br/>(i) √23<br/><br/> (ii) √225 <br/><br/>(iii) 0.3196 <br/><br/>(iv) 7.478478 <br/><br/>(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.