Using a number line, what whole number and rational number to the nearest half is √105 between?
between 10.5 and 11
between 9.5 and 10
between 11 and 11.5
between 10 and 10.5
√105 is approximately 10.246. When rounding to the nearest half, it would be between 10 and 10.5.
To determine which whole number and rational number √105 is between on a number line, we can calculate the approximate value of √105:
√105 is approximately 10.246
Now we can compare this value to the given options:
- Between 10.5 and 11: √105 is smaller than 11 but larger than 10.5.
- Between 9.5 and 10: √105 is larger than 9.5 but smaller than 10.
- Between 11 and 11.5: √105 is smaller than both 11 and 11.5.
- Between 10 and 10.5: √105 is larger than both 10 and 10.5.
Therefore, the correct answer is between 10 and 10.5.