If x, y are both positive rational numbers, then $(\sqrt{x} + \sqrt{y})(\sqrt{x} - \sqrt{y})$ is

1. a rational number
2. an irrational number
3. neither rational nor irrational number
4. both rational as well as irrational number

After rationalising the denominator of $\dfrac{7}{3\sqrt3 - 2\sqrt{2}}$ , we get the denominator as

1. 13
2. 19
3. 5
4. 35

Without actual division, find whether the following rational numbers are terminating decimals or recurring decimals :

$\begin{matrix} \text{(i)} & \dfrac{13}{45} \\[1.5em] \text{(ii)} & -\dfrac{5}{56} \\[1.5em] \text{(iii)} & \dfrac{7}{125} \\[1.5em] \text{(iv)} & -\dfrac{23}{80} \\[1.5em] \text{(v)} & -\dfrac{15}{66} \\[1.5em] \end{matrix}$

In case of terminating decimals, write their decimal expansions.

Express the following recurring decimals as vulgar fractions :

(i) $1.3\overline{45}$

(ii) $2.\overline{357}$