Final answer:
The point on the number line that best represents √10 is B, which is 3.1 because it's the closest square without going over the value of 10.
The correct answer is B.
Step-by-step explanation:
To determine which point on the number line best represents √10, it is helpful to know that the square root of 9 is 3 and the square root of 16 is 4, so √10 must be between 3 and 4. We know that 3.0 is incorrect because 32 is 9, which is too low. To calculate √10 more precisely, we can compare the square of each answer choice with 10. Squaring 3.1 gives us 9.61, squaring 3.2 gives 10.24, squaring 3.3 gives 10.89.
Since 10.24 is the first square over 10, choice C (3.2) is too high, which means option B (3.1), which provides a square of 9.61, slightly under 10, is the best choice.
Therefore, point B at 3.1 on the number line best represents √10 because it is the closest without going over.