Using a number line, what whole number and rational number to the nearest half is
58
−
−
√
between?(1 point)
Responses
The whole number nearest to √58 is 8.
The rational number nearest to √58 is 7.5.
Using rational approximations, what is an inequality statement comparing
81
−
−
√
and
8
–
√
8
? Enter <, >, or =.(1 point)
The inequality is:
81
−
−
√
8
–
√
8
.
The inequality statement comparing \( \sqrt{81} \) and \( \sqrt{8}-\sqrt{8} \) is:
\( \sqrt{81} > \sqrt{8}-\sqrt{8} \)
To find the whole number and rational number to the nearest half that 58√ is between using a number line, follow these steps:
1. Locate the whole number that is closest to 58√ on the number line. Since the square root of a positive whole number is always greater than that number, you can skip this step.
2. Divide the whole number closest to 58√ by 2 to find the nearest half number. In this case, the nearest half number would be 29, since 58 divided by 2 equals 29.
3. Determine if 58√ is greater than or less than the nearest half number. In this case, 58√ is greater than 29.
4. Subtract the nearest half number from 58√ to find the difference. In this case, the difference is 58√ - 29 = 29√.
5. Divide the difference by 2 to find the fraction that is halfway between the whole number and rational number. In this case, the fraction would be (29√) / 2.
Therefore, to the nearest half, 58√ is between 29 and (29√) / 2.