Using a number line, what whole number and rational number to the nearest half is 105√ between?
A: between 10.5 and 11
B: between 9.5 and 10
C: between 10 and 10.5
D: between 11 and 11.5
The square root of any whole number between two consecutive perfect squares will be between the two consecutive whole numbers.
105 is between 100 (10²) and 121 (11²).
So, the square root of 105 is between 10 and 11 on the number line.
To find the nearest half, we look at the decimal value of the square root.
√105 is approximately 10.246.
The nearest half to 10.246 is 10.5.
Therefore, the whole number and rational number to the nearest half that 105√ is between is 10.5 and 11.
So, the answer is A: between 10.5 and 11.