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 the formula for the area of a square

The area \( A \) of a square is given by the formula \( A = s^2 \), where \( s \) is the length of a side. So, to find the side length, we need to solve for \( s \), which gives us \( s=\sqrt{A} \).

Step2: Substitute the given area into the formula

We know that the area \( A = 75 \) square feet. So we need to calculate \( s=\sqrt{75} \).

Step3: Simplify and estimate \( \sqrt{75} \)

We can simplify \( \sqrt{75} \) as \( \sqrt{25\times3}=\sqrt{25}\times\sqrt{3}=5\sqrt{3} \). Since \( \sqrt{3}\approx1.732 \), then \( 5\times1.732 = 8.66 \). So the length of one side is approximately 8.66 feet. If we want a simpler estimate, we know that \( 8^2 = 64 \) and \( 9^2 = 81 \), and 75 is closer to 81 than to 64, so it's a little less than 9, around 8.7 or 8.66.

Answer:

Approximately 8.66 feet (or we can estimate it to be about 9 feet or 8.7 feet depending on the level of estimation needed, but the more precise estimate from the square root is around 8.66).