find the square root of 22.4 by long divison method
Answers
Answer:
The square root of 22.4 is 4.7328638264797. Or,
√22.4 = 4.7328638264797
See, below on this, details on how to calculate this square root using the Babylonian Method
Explanation:
estions like: What is the square root of 22.4 or what is the square root of 22.4?
Use the square root calculator below to find the square root of any imaginary or real number. See also in this web page a Square Root Table from 1 to 100 as well as the Babylonian Method or Hero's Method.
The Babylonian Method also known as Hero's Method
See below how to calculate the square root of 22.4 step-by-step using the Babylonian Method also known as Hero's Method.
In this case we are going to use the 'Babylonian Method' to get the square root of any positive number.
We must set an error for the final result. Say, smaller than 0.001. In other words we will try to find the square root value with at least 2 correct decimal places.
Step 1:
Divide the number (22.4) by 2 to get the first guess for the square root .
First guess = 22.4/2 = 11.2.
Step 2:
Divide 22.4 by the previous result. d = 22.4/11.2 = 2.
Average this value (d) with that of step 1: (2 + 11.2)/2 = 6.6 (new guess).
Error = new guess - previous value = 11.2 - 6.6 = 4.6.
4.6 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 22.4 by the previous result. d = 22.4/6.6 = 3.3939393939.
Average this value (d) with that of step 2: (3.3939393939 + 6.6)/2 = 4.996969697 (new guess).
Error = new guess - previous value = 6.6 - 4.996969697 = 1.603030303.
1.603030303 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 22.4 by the previous result. d = 22.4/4.996969697 = 4.482716798.
Average this value (d) with that of step 3: (4.482716798 + 4.996969697)/2 = 4.7398432475 (new guess).
Error = new guess - previous value = 4.996969697 - 4.7398432475 = 0.2571264495.
0.2571264495 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 22.4 by the previous result. d = 22.4/4.7398432475 = 4.7258946827.
Average this value (d) with that of step 4: (4.7258946827 + 4.7398432475)/2 = 4.7328689651 (new guess).
Error = new guess - previous value = 4.7398432475 - 4.7328689651 = 0.0069742824.
0.0069742824 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 22.4 by the previous result. d = 22.4/4.7328689651 = 4.7328586879.
Average this value (d) with that of step 5: (4.7328586879 + 4.7328689651)/2 = 4.7328638265 (new guess).
Error = new guess - previous value = 4.7328689651 - 4.7328638265 = 0.0000051386.
0.0000051386 <= 0.001. As error <= accuracy, we stop the iterations and use 4.7328638265 as the square root.
So, we can say that the square root of 22.4 is 4.73286 with an error smaller than 0.001 (in fact the error is 0.0000051386). this means that the first 5 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(22.4)' is 4.732863826479693.
Note: There are other ways to calculate square roots. This is only one of them.