If $a = \sqrt{2} + 1$ and $b = \sqrt{2} - 1,$ then the value of $\frac{1}{a + 1} + \frac{1}{b + 1}$ will be

If the cube root of $79507$ is $43$,then the value of $\sqrt[3]{79.507} + \sqrt[3]{0.079507} + \sqrt[3]{0.000079507}$ is

If $M = 0.1 + (0.1)^{2} + (0.001)^{2}$ and $N = 0.3 + (0.03)^{2} + (0.003)^{2}$,then what is the value of $M + N$?

If $\sqrt{x} - \sqrt{y} = 1$ and $\sqrt{x} + \sqrt{y} = 17$,then $\sqrt{xy} = ?$

Which of the following statement$(s)$ is/are $TRUE$?
$I.$ $\sqrt{12} > \sqrt[3]{16} > \sqrt[4]{24}$
$II.$ $\sqrt[3]{25} > \sqrt[4]{32} > \sqrt[6]{48}$
$III.$ $\sqrt[4]{9} > \sqrt[3]{15} > \sqrt[6]{24}$

In a pair of fractions,fraction $A$ is twice the fraction $B$ and the product of the two fractions is $\frac{2}{25}.$ What is the value of fraction $A$?