what whole number and rational number to the nearest half is 105−−−√ between?
To find the whole number and rational number (to the nearest half) that is between $\sqrt{105}$, we need to find the two nearest perfect squares to $105$.
$10^2 = 100$ and $11^2 = 121$, so $105$ is between the perfect squares of $100$ and $121$.
Taking the square roots, we have $10 < \sqrt{105} < 11$.
In terms of halves, $\frac{10}{1} < \sqrt{105} < \frac{11}{1}$.
Therefore, the whole number and rational number to the nearest half that is between $\sqrt{105}$ is $\boxed{\frac{10}{1}}$.
To find the whole number and rational number to the nearest half that 105√ is between, we can calculate the square root and round it to the nearest half.
Step 1: Calculate the square root of 105.
√105 ≈ 10.246950
Step 2: Round the square root to the nearest half.
Rounding 10.246950 to the nearest half gives us 10.5.
Therefore, the whole number and rational number to the nearest half that 105√ is between are 10 and 10.5, respectively.