Using a number line, what whole number and rational number to the nearest half is 58−−√
between?
explain how (between 7.5 and 8) is the correct answer
To determine the whole number and rational number that 58−−√ is between to the nearest half, we can use a number line.
First, we need to find the whole number that is closest to the square root of 58. The square root of 58 is approximately 7.62, so the whole number closest to it is 8.
Next, we check the two neighboring half-values on the number line, namely 7.5 and 8.5.
To determine which one is closer to 58−−√, we can calculate the squares of the differences between each half-value and the square root of 58.
For 7.5, the difference would be (7.5 - √58)² which is approximately 0.0625.
For 8.5, the difference would be (8.5 - √58)² which is approximately 0.0025.
Since 0.0025 is smaller than 0.0625, this means that 8 is closer to 58−−√ than 7.5.
Therefore, 58−−√ is between 7.5 and 8 on the number line, with 8 being the closest whole number and rational number to the nearest half.
To find the whole number and rational number to the nearest half that is between 58 and its square root (√58), we can plot these values on a number line.
First, let's convert the square root of 58 into a decimal. The square root of 58 is approximately 7.62.
On the number line, we can mark the whole numbers, halves, and our calculated values as follows:
- - - 5.5 - - - - 6 - - - 6.5 - - - - - - 7 - - - 7.5 - - - - - - 8 - - - 8.5 - - - - - 9 - - -
We know that the square root of 58 (7.62) lies between 7 and 8. Therefore, we can conclude that the whole number between 58 and its square root to the nearest half is 7.
To find the rational number to the nearest half, we need to compare 58 and 7.5 on the number line.
When we compare 58 (marked after 7) and 7.5 (marked before 8), we can see that the value √58 is closer to 7.5 than to 8. Therefore, the rational number to the nearest half that lies between 58 and its square root is 7.5.
Hence, the whole number is 7, and the rational number to the nearest half is 7.5.