Question

1. a square sandbox has an area of 75 square feet. estimate the length of one of the sides of the sandbox.

Explanation:

Step1: Recall area formula for square

The area formula for a square is $A = s^{2}$, where $A$ is the area and $s$ is the side - length.

Step2: Solve for side - length

Given $A = 75$ square feet, we need to find $s$. So, $s=\sqrt{A}=\sqrt{75}$.
We know that $\sqrt{64}<\sqrt{75}<\sqrt{81}$. Since $\sqrt{64} = 8$ and $\sqrt{81}=9$, $\sqrt{75}$ is between 8 and 9. A closer estimate: $8.5^{2}=72.25$ and $8.7^{2}=75.69$. So, $\sqrt{75}\approx 8.7$ feet.

Answer:

The length of one side of the sandbox is approximately 8.7 feet.