Using a number line, what whole number and rational number to the nearest half is √105 between?(1 point)
Since √105 is between two whole numbers, we can determine which whole numbers it is between by finding the square roots of the numbers surrounding 105.
We know that 105 falls between 100 and 121 because 10^2 = 100 and 11^2 = 121.
Let's find the square roots of these numbers:
√100 = 10
√121 = 11
Now we can determine that √105 is between 10 and 11.
To find the whole number closest to √105, we round to the nearest whole number. In this case, √105 is closer to 11 than 10.
So, the whole number closest to √105 is 11.
To find the rational number to the nearest half, we can think of it as finding the midpoint between 10 and 11. The midpoint is 10.5.
Therefore, the whole number and rational number to the nearest half that √105 is between, is 11 and 10.5 respectively.
To find the whole number and rational number that √105 is between to the nearest half on a number line, we can calculate the square root of 105:
√105 ≈ 10.246
The whole numbers nearest to 10.246 are 10 and 11. Now, let's find the rational numbers nearest to 10.246 to the nearest half.
To the left of 10.246: 9.5
To the right of 10.246: 10.5
Therefore, to the nearest half, √105 is between:
Whole Number: 10
Rational Number: 10.5