Using a number line, what is the approximate value of 19−−√?(1 point)
Responses
4.25
4.25
4.5
4.5
4.13
4.13
4.38
The approximate value of √19 using a number line is 4.38.
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 10.5 and 11
between 10.5 and 11
between 9.5 and 10
between 9.5 and 10
The whole number and rational number to the nearest half between which √105 lies on a number line is between 10.5 and 11.
Using rational approximations, what statement is true?(1 point)
Responses
49−−√<7
start root 49 end root less than 7
48−−√<36−−√
start root 48 end root less than start root 36 end root
49−−√>7
start root 49 end root greater than 7
48−−√>36−−√
start root 48 end root greater than start root 36 end root
The statement that is true when using rational approximations is 49−−√ > 7
To find the approximate value of 19−−√ on a number line, you can start by finding the square root of 19.
To estimate this, you can locate 19 on the number line and then look for the closest perfect square smaller than 19. In this case, the closest perfect square smaller than 19 is 16, which has a square root of 4.
Since the square root of 19 is slightly larger than 4, the answer would be closer to 4.25 or 4.5.
Therefore, the approximate value of 19−−√ would be 4.25 or 4.5.
To find the approximate value of √19 on a number line, you can start by finding the two whole numbers that √19 lies between.
On a number line, you can approximate √19 by finding the square roots of the nearest perfect squares (numbers that can be expressed as the square of an integer). In this case, the nearest square numbers to 19 are 16 and 25. The square root of 16 is 4, and the square root of 25 is 5.
Since 19 is closer to 16, we can assume that √19 is closer to 4 than it is to 5.
Therefore, the approximate value of √19 on a number line is 4.38, which is the midpoint between 4.25 and 4.5.
So the correct answer is 4.38.