Using a number line, what whole number and rational number to the nearest half is 105−−−√
between?
Responses
between 9.5 and 10
between 10 and 10.5
between 11 and 11.5
between 10.5 and 11
The whole number and rational number to the nearest half that 105−−−√ is between is between 10 and 10.5.
can you explain
Sure! To determine which whole number and rational number 105−−−√ is between, we can start by finding the closest whole numbers to the square root of 105.
The square root of 105 is approximately 10.246. The nearest whole numbers to 10.246 are 10 and 11.
Now, we want to find the rational number to the nearest half that is between these two whole numbers.
Between 10 and 11, the halfway point is 10.5. Therefore, the rational number to the nearest half that 105−−−√ is between is 10.5.
To determine which whole number and rational number to the nearest half is between √105, we can estimate its value on a number line.
First, we need to find the square root of 105. The square root of 105 is approximately 10.2469507659.
On the number line, we can locate the whole numbers 10 and 11, and the rational numbers 10.5 and 11.
Since the square root of 105 is closer to 10 than 11, and halfway between 10 and 10.5 is the nearest half, we can conclude that √105 is between 10 and 10.5.
Therefore, the answer is "between 10 and 10.5".