What whole number and rational number to the nearest half is square root 105 between
The square root of 105 is approximately 10.247. The nearest half to this value is 10.5.
The whole number that is nearest to 10.5 is 11.
Therefore, the whole number and rational number to the nearest half that lie between the square root of 105 are 11 and 10.5, respectively.
To find the whole number and rational number to the nearest half that the square root of 105 is between, we can calculate the square roots of the nearest perfect squares.
The nearest perfect squares to 105 are 100 (10^2) and 121 (11^2).
The square root of 100 is 10, and the square root of 121 is 11.
Since √105 is between 10 and 11, the whole number closest to √105 is 11.
To find the rational number to the nearest half, we need to determine if √105 is closer to 10.5 or 11.5.
To do this, we can calculate the value of √105 - 10.5 and √105 - 11.5.
√105 - 10.5 ≈ 10.246
√105 - 11.5 ≈ -0.753
Since √105 - 10.5 is positive and √105 - 11.5 is negative, we can conclude that √105 is closer to 10.5.
Therefore, the whole number to the nearest half that √105 is between is 11, and the rational number to the nearest half is 10.5.