Using a number line, what whole number and rational number to the nearest half is 68−−√
between?(1 point)
The whole number closest to √68 is 8, since √68 is between √64 (which is 8) and √81 (which is 9).
To find the rational number closest to √68 to the nearest half, we can look at the halves between 8 and 9.
The halves between 8 and 9 are 8.0, 8.5, and 9.0.
Since √68 is closer to 8.5 than to 8 or 9, the rational number closest to √68 to the nearest half is 8.5.
To determine the whole number and rational number to the nearest half for √68, we need to find the whole number and rational number that is closest to the square root of 68.
First, we find the square root of 68:
√68 ≈ 8.246211
The whole number closest to 8.246211 is 8.
Next, we need to find the rational number to the nearest half. The nearest half can be either 0.5 or -0.5.
To determine which one is closer to √68, we can compare the distance between √68 and 8.5 and the distance between √68 and 8. If the distance between √68 and 8.5 is smaller, then 8.5 is the rational number to the nearest half. Otherwise, if the distance between √68 and 8 is smaller, then 8 is the rational number to the nearest half.
Distance between √68 and 8.5:
|√68 - 8.5| ≈ 0.253789
Distance between √68 and 8:
|√68 - 8| ≈ 0.246211
Since the distance between √68 and 8 is smaller, the rational number closest to √68 to the nearest half is 8.
Therefore, the whole number closest to √68 is 8, and the rational number to the nearest half is also 8.