Solve the given two equations and choose the correct answer from the given options.
$I.$ $x^{2} = 729$
$II.$ $y = \sqrt{729}$

Solve the given two equations and select the correct answer from the given options.
$I.$ $\sqrt{784} x + 1234 = 1486$
$II.$ $\sqrt{1089} y + 2081 = 2345$

If $x$ is a solution of the equation $\sqrt{2x + 1} - \sqrt{2x - 1} = 1$ where $x \ge \frac{1}{2}$,then $\sqrt{4x^2 - 1}$ is equal to:

Construct a quadratic equation whose roots are $\sqrt{2}$ and $2 \sqrt{2}$.

Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up with roots $(4, 3).$ Rahul made a mistake in writing down the coefficient of $x$ and got roots $(3, 2).$ The correct roots of the equation are:

The solution set of the equation $x^{\log_x(1 - x)^2} = 9$ is