sqaure root of 21.92 with solution
Answers
Answer:
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Step-by-step explanation:
The square root of 21.92 is 4.6818799642878. Or,
√21.92 = 4.6818799642878
See, below on this web page, details on how to calculate this square root using the Babylonian Method
Answer:
Step 1:
Divide the number (21.92) by 2 to get the first guess for the square root .
First guess = 21.92/2 = 10.96.
Step 2:
Divide 21.92 by the previous result. d = 21.92/10.96 = 2.
Average this value (d) with that of step 1: (2 + 10.96)/2 = 6.48 (new guess).
Error = new guess - previous value = 10.96 - 6.48 = 4.48.
4.48 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 21.92 by the previous result. d = 21.92/6.48 = 3.3827160494.
Average this value (d) with that of step 2: (3.3827160494 + 6.48)/2 = 4.9313580247 (new guess).
Error = new guess - previous value = 6.48 - 4.9313580247 = 1.5486419753.
1.5486419753 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 21.92 by the previous result. d = 21.92/4.9313580247 = 4.4450230322.
Average this value (d) with that of step 3: (4.4450230322 + 4.9313580247)/2 = 4.6881905285 (new guess).
Error = new guess - previous value = 4.9313580247 - 4.6881905285 = 0.2431674962.
0.2431674962 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 21.92 by the previous result. d = 21.92/4.6881905285 = 4.6755778944.
Average this value (d) with that of step 4: (4.6755778944 + 4.6881905285)/2 = 4.6818842115 (new guess).
Error = new guess - previous value = 4.6881905285 - 4.6818842115 = 0.006306317.
0.006306317 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 21.92 by the previous result. d = 21.92/4.6818842115 = 4.6818757171.
Average this value (d) with that of step 5: (4.6818757171 + 4.6818842115)/2 = 4.6818799643 (new guess).
Error = new guess - previous value = 4.6818842115 - 4.6818799643 = 0.0000042472.
0.0000042472 <= 0.001. As error <= accuracy, we stop the iterations and use 4.6818799643 as the square root.
So, we can say that the square root of 21.92 is 4.68187 with an error smaller than 0.001 (in fact the error is 0.0000042472). this means that the first 5 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(21.92)' is 4.68187996428785.
Note: There are other ways to calculate square roots. This is only one of them.
Step-by-step explanation:
how it helps you