square root of 1344 by long division method
Answers
Here is the answer to questions like: Square root of 1344 or what is the square root of 1344?
Note:you can write any one step you like.
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 1344 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 (1344) by 2 to get the first guess for the square root .
First guess = 1344/2 = 672.
Step 2:
Divide 1344 by the previous result. d = 1344/672 = 2.
Average this value (d) with that of step 1: (2 + 672)/2 = 337 (new guess).
Error = new guess - previous value = 672 - 337 = 335.
335 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 1344 by the previous result. d = 1344/337 = 3.9881305638.
Average this value (d) with that of step 2: (3.9881305638 + 337)/2 = 170.4940652819 (new guess).
Error = new guess - previous value = 337 - 170.4940652819 = 166.5059347181.
166.5059347181 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 1344 by the previous result. d = 1344/170.4940652819 = 7.8829723356.
Average this value (d) with that of step 3: (7.8829723356 + 170.4940652819)/2 = 89.1885188087 (new guess).
Error = new guess - previous value = 170.4940652819 - 89.1885188087 = 81.3055464732.
81.3055464732 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 1344 by the previous result. d = 1344/89.1885188087 = 15.0692041751.
Average this value (d) with that of step 4: (15.0692041751 + 89.1885188087)/2 = 52.1288614919 (new guess).
Error = new guess - previous value = 89.1885188087 - 52.1288614919 = 37.0596573168.
37.0596573168 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 1344 by the previous result. d = 1344/52.1288614919 = 25.7822626763.
Average this value (d) with that of step 5: (25.7822626763 + 52.1288614919)/2 = 38.9555620841 (new guess).
Error = new guess - previous value = 52.1288614919 - 38.9555620841 = 13.1732994078.
13.1732994078 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 1344 by the previous result. d = 1344/38.9555620841 = 34.500849894.
Average this value (d) with that of step 6: (34.500849894 + 38.9555620841)/2 = 36.728205989 (new guess).
Error = new guess - previous value = 38.9555620841 - 36.728205989 = 2.2273560951.
2.2273560951 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 1344 by the previous result. d = 1344/36.728205989 = 36.5931295529.
Average this value (d) with that of step 7: (36.5931295529 + 36.728205989)/2 = 36.660667771 (new guess).
Error = new guess - previous value = 36.728205989 - 36.660667771 = 0.067538218.
0.067538218 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 1344 by the previous result. d = 1344/36.660667771 = 36.6605433484.
Average this value (d) with that of step 8: (36.6605433484 + 36.660667771)/2 = 36.6606055597 (new guess).
Error = new guess - previous value = 36.660667771 - 36.6606055597 = 0.0000622113.
0.0000622113 <= 0.001. As error <= accuracy, we stop the iterations and use 36.6606055597 as the square root.
So, we can say that the square root of 1344 is 36.6606 with an error smaller than 0.001 (in fact the error is 0.0000622113). this means that the first 4 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(1344)' is 36.66060555964672.
Note: There are other ways to calculate square roots. This is only one of them.