#### Answer

$5\sqrt2 \times 5\sqrt2 \times \sqrt2$ inches
or approximately
$7.07 \times 7.07 \times 7.07$ inches

#### Work Step by Step

The surface area of a cube is equal to six times the area of one side (or one face).
Each side/face of a cube is a square whose area is equal the square of its side length.
Thus, if the surface area of a cube-shaped jewelry box is $300$ square inches, then the area of each side/face of the jewelry box is:
\begin{align*}
&=\frac{300}{6}
\\&=50\text{ square inches}
\end{align*}
If we let $x$= side length of the square, then:
\begin{align*}
x^2&=50\\
\sqrt{x^2}&=\sqrt{50}\\
x&=\sqrt{25(2)}\\
x&=5\sqrt2\approx 7.07 \text{ inches}
\end{align*}
Therefore, the dimensions of the jewelry box are :
$5\sqrt2 \times 5\sqrt2 \times \sqrt2$ inches or approximately $7.07 \times 7.07 \times 7.07$ inches