Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?(1 point)
Responses
between 11 and 11.5
between 10.5 and 11
between 9.5 and 10
between 10 and 10.5
To determine which whole number and rational number the square root of 105 is between, we can use approximation. The square root of 105 is approximately 10.25.
Therefore, the whole number and rational number to the nearest half that the square root of 105 is between are:
between 10 and 10.5
To find the whole number and rational number closest to √105, let's use a number line:
On the number line, we can find that √100 is 10 and √121 is 11.
Since √105 is between 10 and 11, we can find the rational number closest to √105 by finding the halfway point between these two whole numbers.
10 + (1/2) = 10.5
Therefore, the whole number and rational number closest to √105 to the nearest half is between 10.5 and 11.