Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?(1 point)
Responses
between 10 and 10.5
between 10 and 10.5
between 11 and 11.5
between 11 and 11.5
between 9.5 and 10
between 9.5 and 10
between 10.5 and 11
between 10.5 and 11
Using rational approximations, what statement is true?(1 point)
49−−√>7
start root 49 end root greater than 7
48−−√>36−−√
start root 48 end root greater than start root 36 end root
48−−√<36−−√
start root 48 end root less than start root 36 end root
49−−√<7
start root 49 end root is less than 7
To find the whole number and rational number to the nearest half for √105, let's start by finding the whole number that is closest to √105.
We know that √100 = 10 and √121 = 11, so √105 must be between these two numbers.
Next, let's find the rational number to the nearest half. Since √105 is between 10 and 11 on the number line, we need to find the number that is halfway between them.
To find the halfway point between 10 and 11, we can add them together and divide by 2:
(10 + 11) / 2 = 21 / 2 = 10.5
Therefore, the whole number and rational number to the nearest half for √105 on the number line is between 10 and 10.5.
To solve this problem, we need to find the whole number and rational number that is closest to the square root of 105.
First, let's find the square root of 105. Using a calculator or any mathematical software, we get approximately 10.247.
Now, let's look at the number line:
_________|_________|_________|_________|_________
9.5 10 10.5 11 11.5 12
Since the square root of 105 is approximately 10.247, we can see that it falls between 10 and 10.5.
Therefore, the whole number and rational number to the nearest half that 105^(-−√) is between is 10 and 10.5.