Using a number line, what is the approximate value of square root 19
A. 4.38
B. 4.5
C. 4.13
D. 4.25
To determine the approximate value of square root 19 using a number line, we need to locate the number 19 on the number line and estimate the value of the square root.
A number line can be drawn and labeled with the relevant numbers, but it is difficult to display accurately in this text-based format. However, we can still use a number line conceptually. We know that 16 is a perfect square, and it is less than 19, so let's place it on the number line. We can also place 25, which is the next perfect square after 19.
On the number line, we have:
16 -------- ? --------- 19 -------- ? --------- 25
Now, we can see that 19 is closer to 16 than it is to 25, suggesting that the square root of 19 should be closer to the square root of 16, which is 4, than to the square root of 25, which is 5.
So, the approximate value of square root 19 is 4.
To find the approximate value of the square root of 19 on a number line, we can look for two consecutive whole numbers between which 19 lies.
Let's start by finding the square of whole numbers and their corresponding square roots:
1^2 = 1, √1 ≈ 1
2^2 = 4, √4 = 2
3^2 = 9, √9 = 3
4^2 = 16, √16 = 4
From here, we can see that the square root of 19 falls between the whole numbers 4 and 5, because 19 is greater than 16 (4 squared) but less than 25 (5 squared).
Now, we can estimate the value on the number line. The difference between 4 and 5 is 1. We divide the distance between them into 10 equal parts.
4 _______ _____ _____ _____ _____ _____ _____ _____ _____ 5
Since the approximate value of 19 lies closer to 4, we can estimate it between the fourth and fifth tick marks:
4 _______ _____ _____ + _____ _____ _____ _____ _____ 5
Therefore, the approximate value of the square root of 19 on the number line is between 4.3 and 4.4.
Among the given options, the closest approximate value is 4.38 (option A).