Two-fifth of one-fourth of three-seventh of a number is $15$. What is half of that number?

If we multiply a fraction by itself and divide the product by its reciprocal,the fraction thus obtained is $18 \frac{26}{27}$. The original fraction is

What is the value of $\left[\frac{12}{(\sqrt{5}+\sqrt{3})}+\frac{18}{(\sqrt{5}-\sqrt{3})}\right]$?

Which of the following is true?
$I.$ $\frac{1}{\sqrt[3]{12}} > \frac{1}{\sqrt[4]{29}} > \frac{1}{\sqrt{5}}$
$II.$ $\frac{1}{\sqrt[4]{29}} > \frac{1}{\sqrt[3]{12}} > \frac{1}{\sqrt{5}}$
$III.$ $\frac{1}{\sqrt{5}} > \frac{1}{\sqrt[3]{12}} > \frac{1}{\sqrt[4]{29}}$
$IV.$ $\frac{1}{\sqrt{5}} > \frac{1}{\sqrt[4]{29}} > \frac{1}{\sqrt[3]{12}}$

$\frac{4.2 \times 4.2 - 1.9 \times 1.9}{2.3 \times 6.1} = ?$

If $x = \sqrt{3} + \frac{1}{\sqrt{3}}$,then the value of $\left(x - \frac{\sqrt{126}}{\sqrt{42}}\right) + \left(x - \frac{1}{x - \frac{2\sqrt{3}}{3}}\right)$ is