Which of the following is a common approximation for the square root of 10?

The common approximation for the square root of 10 is approximately 3.16, which is why this choice is considered correct. To understand this, we can look at the mathematical context. The square root of 10 lies between the squares of 3 and 4, as (3^2 = 9) and (4^2 = 16). Since 10 is closer to 9 than to 16, we approximate that the square root should be a little more than 3.

Calculating more explicitly, the square root of 10 is about 3.162. When rounding to two decimal places, this gives us approximately 3.16, which makes it a good estimate for general use. This understanding aligns well with both numerical methods and basic calculator use, where you might often find the square root of 10 rounded to 3.16.

This approximation is useful in various math applications, allowing quick estimations without needing a calculator for precise values. The other values listed are further from the true square root of 10 and would not be as reliable for approximation purposes.