(i) \(\sqrt4 = 2 = \frac{2}{1}\)
\(\sqrt4\) can be written in the form of \(\frac{p}q\), so it is a rational number. Its decimal expansion is 2.0
(ii) \(3\sqrt{18}\) \(= 3\sqrt{{2 \times 3\times 3}}\)
\(=3 \times 3 \sqrt2\)
\(= 9\sqrt2\)
Since, the product of a rational and an irrational is an irrational number.
Therefore,\(9\sqrt2\) is an irrational;
\(3\sqrt{18}\) is an irrational number
(iii) We have,
\(\sqrt{1.44}\) \(= \frac{12}{10}\)
= 1.2
Every terminating decimal is a rational number, so 1.2 is a rational number.
(iv) we have,
\(\sqrt\frac{9}{27}\) \(= \frac{3}{\sqrt{27}}\) \(\frac{3}{\sqrt{3\times 3\times 3}}\)
\(= \frac{1}{3}\)
Quotient of a rational and an irrational number is irrational number. Therefore, it is an irrational number.
(v) -\(\sqrt{64}\) \(= - \sqrt{8\times8}\)
= - 8 = -8/1
AS it can be expressed in the form of \(\frac{p}q,\) so it is a rational number
(vi) \(\sqrt{100}\) = 10 = \(\frac{10}{1}\)
Thus it can be expressed in the form of \(\frac{p}q,\) so it is a rational number.