If $\sqrt{2}=1.4142,$ then $\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}$ is equal to

Show that $0 . \overline{142857}=\frac{1}{7}$

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0 .$

$0 . \overline{35}$

For each question, select the proper option from four options given, to make the statement true : (Final answer only)

$(\sqrt{5}+3)^{2}$ is a $/$ an $\ldots \ldots \ldots$ number.

Rationalise the denominator of the following:

$\frac{2+\sqrt{3}}{2-\sqrt{3}}$

If $\left(\frac{2}{5}\right)^{5} \times\left(\frac{25}{4}\right)^{3}=\left(\frac{5}{2}\right)^{3 x-2},$ then find $x$.