If $\sqrt{2} = 1.4142$,then evaluate $\sqrt{5} \div \sqrt{10}$ correct to four decimal places.

Find the value of $\left(\frac{1}{27}\right)^{-\frac{2}{3}}$.

For each question,select the proper option from four options given,to make the statement true: The decimal expansion of $-\frac{11}{4}$ is..........

After rationalizing the denominator of $\frac{7}{3 \sqrt{3}-2 \sqrt{2}},$ we get the denominator as

Rationalise the denominator of the following:
$\frac{3+\sqrt{2}}{4 \sqrt{2}}$

Let $x$ and $y$ be rational and irrational numbers,respectively. Is $x+y$ necessarily an irrational number? Give an example in support of your answer.