the square of 712 is
Answers
Answer:
The square root of 712 is 26.68332812825267. Or,
√712 = 26.68332812825267
Step-by-step explanation:
Step 1:
Divide the number (712) by 2 to get the first guess for the square root .
First guess = 712/2 = 356.
Step 2:
Divide 712 by the previous result. d = 712/356 = 2.
Average this value (d) with that of step 1: (2 + 356)/2 = 179 (new guess).
Error = new guess - previous value = 356 - 179 = 177.
177 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 712 by the previous result. d = 712/179 = 3.9776536313.
Average this value (d) with that of step 2: (3.9776536313 + 179)/2 = 91.4888268157 (new guess).
Error = new guess - previous value = 179 - 91.4888268157 = 87.5111731843.
87.5111731843 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 712 by the previous result. d = 712/91.4888268157 = 7.7823710805.
Average this value (d) with that of step 3: (7.7823710805 + 91.4888268157)/2 = 49.6355989481 (new guess).
Error = new guess - previous value = 91.4888268157 - 49.6355989481 = 41.8532278676.
41.8532278676 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 712 by the previous result. d = 712/49.6355989481 = 14.3445433336.
Average this value (d) with that of step 4: (14.3445433336 + 49.6355989481)/2 = 31.9900711409 (new guess).
Error = new guess - previous value = 49.6355989481 - 31.9900711409 = 17.6455278072.
17.6455278072 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 712 by the previous result. d = 712/31.9900711409 = 22.2569058026.
Average this value (d) with that of step 5: (22.2569058026 + 31.9900711409)/2 = 27.1234884718 (new guess).
Error = new guess - previous value = 31.9900711409 - 27.1234884718 = 4.8665826691.
4.8665826691 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 712 by the previous result. d = 712/27.1234884718 = 26.2503107128.
Average this value (d) with that of step 6: (26.2503107128 + 27.1234884718)/2 = 26.6868995923 (new guess).
Error = new guess - previous value = 27.1234884718 - 26.6868995923 = 0.4365888795.
0.4365888795 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 712 by the previous result. d = 712/26.6868995923 = 26.6797571422.
Average this value (d) with that of step 7: (26.6797571422 + 26.6868995923)/2 = 26.6833283673 (new guess).
Error = new guess - previous value = 26.6868995923 - 26.6833283673 = 0.003571225.
0.003571225 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 712 by the previous result. d = 712/26.6833283673 = 26.6833278892.
Average this value (d) with that of step 8: (26.6833278892 + 26.6833283673)/2 = 26.6833281283 (new guess).
Error = new guess - previous value = 26.6833283673 - 26.6833281283 = 2.39e-7.
2.39e-7 <= 0.001. As error <= accuracy, we stop the iterations and use 26.6833281283 as the square root.
So, we can say that the square root of 712 is 26.683328 with an error smaller than 0.001 (in fact the error is 2.39e-7). this means that the first 6 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(712)' is 26.68332812825267.