A square garden has an area of 50 square meters. Estimate its side length to the nearest tenth of a meter.
The problem asks for the side length \(s\) of a square garden with a known area \(A = 50 \text{ m}^2\). The area of a square is calculated using the formula \(A = s^2\), where \(s\) is the side length of the square. Given that \(A = 50\), we have the equation \(s^2 = 50\). To find the side length, we need to take the square root of both sides, so \(s = \sqrt{50}\).
To estimate \(\sqrt{50}\), we can look for perfect squares near 50. We know that \(7^2 = 49\) and \(8^2 = 64\). Since 50 is very close to 49, we expect \(\sqrt{50}\) to be slightly larger than 7. By testing the square of 7.1:
\((7.1)^2 = 7.1 \times 7.1 = 50.41\).
By testing the square of 7.0:
\((7.0)^2 = 7.0 \times 7.0 = 49.00\).
Since 50.41 is closer to 50 than 49.00 is, we find that the side length \(s \approx 7.1\) meters.
The value of \(\sqrt{50}\) is approximately 7.071. When rounding to the nearest tenth, we look at the hundredths digit, which is 7. Since 7 is 5 or greater, we round up the tenths digit from 0 to 1. Thus, the side length of the square garden to the nearest tenth of a meter is 7.1 meters. The final answer is \(\boxed{7.1 \text{ m}}\).
Estimating side lengths is a vital skill for anyone working in landscaping or home improvement. For example, if you are planning to build a square garden bed and you know exactly how much space it covers in square meters, calculating the side length helps you determine how much fencing you need to buy to enclose it. In this case, for a 50 square meter garden, you would need enough fencing for a perimeter of approximately \(4 \times 7.1 = 28.4\) meters.