Using a number line, what is the approximate value of 19 Square root
To find the approximate value of √19 using a number line, we can plot the numbers and estimate where √19 falls between two whole numbers.
On a number line, locate the numbers 4 and 5 (because 4² = 16 and 5² = 25).
0 1 2 3 4 5 6
----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|--
-6 -5 -4 -3 -2 -1 0 1 2 3 4
Since 19 is greater than 16 (4²) but less than 25 (5²), we can estimate that √19 lies closer to 4 than it does to 5.
Therefore, the approximate value of √19 on the number line is closer to 4.
To find the approximate value of √19 using a number line, we can follow these steps:
1. Draw a number line and mark the integers on it.
-5 -4 -3 -2 -1 0 1 2 3 4 5
2. Locate the value of 19 on the number line. Since 19 is between 4 and 5, we can estimate it as 4.5.
-5 -4 -3 -2 -1 0 1 2 3 4 5
^
4
3. Now, let's find the square root of 4.5. We can estimate the value by halving it.
4.5 ÷ 2 = 2.25
4. Repeat the process of dividing by 2 and getting the average until we get the desired approximation:
2.25 ÷ 2 = 1.125
1.125 ÷ 2 = 0.5625
0.5625 ÷ 2 = 0.28125
After a few iterations, we can approximate the square root of 19 to be around 4.358.