Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
58−−√ is between ___ and ___
To determine the whole number and rational number to the nearest half that √58 is between, we need to find the two numbers on the number line that √58 is closest to.
To do this, we can find the whole number and rational number that are closest to both the left and right sides of √58 on the number line.
First, let's find the whole number. The perfect square roots of whole numbers are only found at 0, 1, 4, 9, 16, 25, etc. The nearest perfect square root below 58 is √49, which equals 7. Therefore, √58 is closer to 7 than it is to 6.
Next, let's find the rational number to the nearest half. The whole number part of √58 is 7, so we need to determine if √58 is closer to 7 or 8 on the number line. To do this, we can compare the distance between √58 and 7.5, and the distance between √58 and 6.5.
Calculating these distances, we find that the distance between √58 and 7.5 is approximately 0.0858, while the distance between √58 and 6.5 is approximately 0.0854. Thus, the distance from √58 to 7.5 is larger, indicating that √58 is closer to 7 than it is to 8.
Therefore, the whole number and rational number to the nearest half that √58 is between is 7 and 7.5 respectively.
In summary, √58 is between 7 and 7.5 when using a number line.