The nearest approximate value of $\sqrt{2023}$ is

The approximate change in the volume $V$ of a cube of side $x$ meters caused by increasing the side by $3\%$ is: (in $x^{3} \text{ m}^{3}$)

$A$ point on the hypotenuse of a triangle is at distances $a$ and $b$ from the sides of the triangle. Show that the minimum length of the hypotenuse is $(a^{\frac{2}{3}}+b^{\frac{2}{3}})^{\frac{3}{2}}$.

Find the approximate value of $(1.999)^{5}$.

Find the approximate value of $(0.009)^{\frac{1}{3}}$.

Find the approximate value of $(401)^{\frac{1}{2}}$.