Simply square root of 4

The square root of 4 is 2.

The volume \( V \) of a cube is given by the formula:

\[ V = s^3 \]

where \( s \) is the length of each side of the cube.

Given that the volume is \( \frac{125}{8} \) ft³, we can set up the equation:

\[ s^3 = \frac{125}{8} \]

To find \( s \), we take the cube root of both sides:

\[ s = \sqrt[3]{\frac{125}{8}} \]

Calculating this:

\[ s = \frac{\sqrt[3]{125}}{\sqrt[3]{8}} = \frac{5}{2} \]

Thus, the length of each side of the cardboard box is \( \frac{5}{2} \) ft or 2.5 ft.

The length of each side of the cardboard box is \( \frac{5}{2} \) ft.

To solve the equation \( x^2 = \frac{24}{9} \), first simplify the fraction:

\[ \frac{24}{9} = \frac{8}{3} \]

Now, we have:

\[ x^2 = \frac{8}{3} \]

Next, take the square root of both sides:

\[ x = \pm \sqrt{\frac{8}{3}} \]

To simplify \( \sqrt{\frac{8}{3}} \):

\[ x = \pm \frac{\sqrt{8}}{\sqrt{3}} = \pm \frac{2\sqrt{2}}{\sqrt{3}} = \pm \frac{2\sqrt{6}}{3} \]

Thus, the solutions for \( x \) are:

\[ x = \frac{2\sqrt{6}}{3} \quad \text{or} \quad x = -\frac{2\sqrt{6}}{3} \]

The solution for \( x \) is \( \frac{2\sqrt{6}}{3} \).

I apologize for any confusion. Let's solve the equation step by step clearly.

Given:

\[ x^2 = \frac{24}{9} \]

First, simplify \( \frac{24}{9} \):

\[ \frac{24}{9} = \frac{8}{3} \]

Now the equation is:

\[ x^2 = \frac{8}{3} \]

Taking the square root of both sides gives us:

\[ x = \sqrt{\frac{8}{3}} \quad \text{or} \quad x = -\sqrt{\frac{8}{3}} \]

Now simplifying \( \sqrt{\frac{8}{3}} \):

\[ \sqrt{\frac{8}{3}} = \frac{\sqrt{8}}{\sqrt{3}} = \frac{2\sqrt{2}}{\sqrt{3}} \]

Converting this into a decimal form:

\[ \sqrt{8} \approx 2.828 \quad \text{and} \quad \sqrt{3} \approx 1.732 \]

Thus,

\[ x \approx \frac{2.828}{1.732} \approx 1.632 \]

So the positive solution is approximately \( 1.632 \).

If you need the exact solution without alternatives, it is:

The positive value of \( x \) is \( \frac{2\sqrt{2}}{\sqrt{3}} \).

If neither of these forms is acceptable, kindly provide the specific options to clarify.