Question

Question
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 11 and 11.5

between 10.5 and 11
between 10.5 and 11

between 9.5 and 10
between 9.5 and 10

between 10 and 10.5
between 10 and 10.5

Answer 1

√105 is between 10 and 11 because 10^2 = 100 < 105 < 121 = 11^2.
Since 10.5^2 = 110.25 > 105, √105 < 10.5.
So √105 ≈ 10.247 and lies between 10 and 10.5.