Question

Which of the following is an irrational number?

(a) $\sqrt{\frac{9}{27}}$

(b) −$\sqrt{64}$

(c) $\sqrt{1.44}$

(d) $\sqrt{\frac{1}{4}}$

Answer 1

Let us simplify each of the numbers $\sqrt{\frac{9}{27}}$, −$\sqrt{64}$, $\sqrt{1.44}$ and $\sqrt{\frac{1}{4}}$ separately.
$$\begin{gathered} \sqrt{\frac{9}{27}}=\sqrt{\frac{1}{3}}=\frac{1}{\sqrt{3}} \\ -\sqrt{64}=-\sqrt{8\times 8}=-8 \\ \sqrt{1.44}=\sqrt{\frac{144}{100}}=\frac{12}{10}=1.2 \\ \sqrt{\frac{1}{4}}=\frac{1}{\sqrt{4}}=\frac{1}{2} \end{gathered}$$
Here, −$\sqrt{64}$, $\sqrt{1.44}$ and $\sqrt{\frac{1}{4}}$ are rational numbers while $\sqrt{\frac{9}{27}}$ is an irrational number.
Hence, the correct option is (a).