Answer:
To approximate the location of the square root of 14 on a number line, we can first find the two integers that √14 is between. We know that:
3^2 = 9 < 14 < 16 = 4^2
So √14 is between 3 and 4. We can divide the distance between 3 and 4 into equal parts and estimate the location of √14 based on where it falls in that interval.
Dividing the interval into 10 equal parts, we get:
3.0 - 3.1 - 3.2 - 3.3 - 3.4 - 3.5 - 3.6 - 3.7 - 3.8 - 3.9 - 4.0
Since √14 is closer to 3 than to 4, we can estimate its location as being closer to 3.4 than to 3.5. Therefore, a good approximation for the location of √14 on the number line is 3.7.