Final answer:
The whole number closest to the square root of 58 is 8, and the rational number to the nearest half is 7.5 on the number line.
Step-by-step explanation:
The student's question asks about the whole number and rational number to the nearest half that are closest to the square root of 58 on the number line. First, we can establish that the square root of 58 is somewhere between 7 and 8, since 7² = 49 and 8² = 64, and 58 falls between these two squares. Now, to find the rational number to the nearest half, we look for halves that are between 7 and 8. These are 7.5 and 8.0. Since the square root of 58 is closer to 8 than it is to 7, we know it is also closer to 7.5 than to 8. Thus, the rational number to the nearest half would be 7.5.
Next, we notice that the square root falls closer to 8 than 7, making 8 the nearest whole number. Hence, the whole number closest to √58 on the number line is 8, and the rational number to the nearest half is 7.5. When working with numbers graphically, like on a number line, it’s important to consider the context of how you round numbers, similar to how you would keep the number of decimal places the same as those in the original numbers when calculating and rounding your final answers.