To find a whole number and rational number to the nearest half that √107 is between, we can square different numbers until we find a square that is close to 107.
Let's start with the first given range, between 9.5 and 10:
9.5^2 = 90.25
10^2 = 100
Since 107 is between these two squares, we know that the square root of 107 (√107) is between 9.5 and 10.
Therefore, the whole number to the nearest half is 10.
Between 10.5 and 11:
10.5^2 = 110.25
11^2 = 121
Since 107 is between these two squares, √107 is between 10.5 and 11.
Therefore, the whole number to the nearest half is 11.
Between 10 and 10.5:
10^2 = 100
10.5^2 = 110.25
Since 107 is between these two squares, √107 is between 10 and 10.5.
Therefore, the whole number to the nearest half is 10.
Between 11 and 11.5:
11^2 = 121
11.5^2 = 132.25
Since 107 is between these two squares, √107 is between 11 and 11.5.
Therefore, the whole number to the nearest half is 11.
In summary:
√107 is between:
- 9.5 and 10, so the whole number to the nearest half is 10.
- 10.5 and 11, so the whole number to the nearest half is 11.
- 10 and 10.5, so the whole number to the nearest half is 10.
- 11 and 11.5, so the whole number to the nearest half is 11.
Using a number line what whole number and rational number to the nearest half is √ 107 between
Between 9.5 and 10
Between 10.5 and 11
Between 10 and 10.5
Between 11 and 11.5
3 answers
Answer is
√107 is between 10 and 10.5 on the number line. Therefore, the whole number to the nearest half is 10 and the rational number to the nearest half is 10.5.
1 answer