Using a number line, what whole number and rational number to the nearest half is sqrt(105) between? (1 point)
O between 10 and 10.5
O between 11 and 11.5
O between 9.5 and 10
O between 10.5 and 11
To determine the whole number and rational number to the nearest half that sqrt(105) is between, we need to find the two consecutive numbers whose squares are closest to 105.
The square root of 105 is approximately 10.247.
Calculating the squares of the numbers between 10 and 11:
10 squared = 100
11 squared = 121
Since 105 is closer to 100 than to 121, sqrt(105) is between 10 and 11.
Therefore, the correct answer is: between 10 and 10.5 (O).
To determine the whole number and rational number nearest to √105 using a number line, we need to find √105 and its surrounding half values.
Calculating √105, we find that it is approximately 10.246.
Looking at the given options:
- Between 10 and 10.5: √105 is greater than 10.
- Between 11 and 11.5: √105 is less than 11.
- Between 9.5 and 10: √105 is greater than 9.5.
- Between 10.5 and 11: √105 is less than 10.5.
Based on this information, we can conclude that √105 is between 10 and 10.5.
Therefore, the correct answer is: O between 10 and 10.5.