Using a number line, what is the approximate value of 19−−√?(1 point)
Responses
'
4.25
4.5
4.38
4.13
The approximate value of √19 on a number line is 4.38.
To approximate the value of √19 on a number line, we can start by finding the square root of 19 manually:
√16 = 4
√25 = 5
Since 19 falls between 16 and 25, we know that √19 will fall between 4 and 5 on the number line. To get a more precise approximation, we can divide the difference between 4 and 5 into smaller parts. Let's divide it into tenths:
4.0, 4.1, 4.2, 4.3, 4.4, 4.5
We know that √19 is closer to 4.5 than it is to 4.4 because 4.4 squared is 19.36 (which is greater than 19) and 4.5 squared is 20.25 (which is greater than 19 as well). Therefore, the approximate value of √19 on the number line is 4.5.