Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?(1 point)
Responses
between 9.5 and 10
between 9.5 and 10
between 10.5 and 11
between 10.5 and 11
between 10 and 10.5
between 10 and 10.5
between 11 and 11.5
The rational number that is closest, but not equal, to the square root of 105 is between 10 and 10.5 on the number line. The whole number that is closest, but not equal, to the square root of 105 is 10.
To find the whole number and rational number nearest to √105, let's first calculate the value of √105:
√105 ≈ 10.246
Now, let's look at the number line:
9--9.5--10--10.5--11--11.5--12
√105 is between 10 and 10.5. Therefore, the whole number and rational number nearest to √105 to the nearest half are:
between 10 and 10.5.