square root of 52900
Answers
Step-by-step explanation:
230 is the correct answer.....
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Answer:
230
Step-by-step explanation:
Step 1:
Divide the number (52900) by 2 to get the first guess for the square root .
First guess = 52900/2 = 26450.
Step 2:
Divide 52900 by the previous result. d = 52900/26450 = 2.
Average this value (d) with that of step 1: (2 + 26450)/2 = 13226 (new guess).
Error = new guess - previous value = 26450 - 13226 = 13224.
13224 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 52900 by the previous result. d = 52900/13226 = 3.9996975654.
Average this value (d) with that of step 2: (3.9996975654 + 13226)/2 = 6614.9998487827 (new guess).
Error = new guess - previous value = 13226 - 6614.9998487827 = 6611.0001512173.
6611.0001512173 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 52900 by the previous result. d = 52900/6614.9998487827 = 7.9969767512.
Average this value (d) with that of step 3: (7.9969767512 + 6614.9998487827)/2 = 3311.498412767 (new guess).
Error = new guess - previous value = 6614.9998487827 - 3311.498412767 = 3303.5014360157.
3303.5014360157 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 52900 by the previous result. d = 52900/3311.498412767 = 15.9746415085.
Average this value (d) with that of step 4: (15.9746415085 + 3311.498412767)/2 = 1663.7365271378 (new guess).
Error = new guess - previous value = 3311.498412767 - 1663.7365271378 = 1647.7618856292.
1647.7618856292 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 52900 by the previous result. d = 52900/1663.7365271378 = 31.7958998538.
Average this value (d) with that of step 5: (31.7958998538 + 1663.7365271378)/2 = 847.7662134958 (new guess).
Error = new guess - previous value = 1663.7365271378 - 847.7662134958 = 815.970313642.
815.970313642 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 52900 by the previous result. d = 52900/847.7662134958 = 62.3992784306.
Average this value (d) with that of step 6: (62.3992784306 + 847.7662134958)/2 = 455.0827459632 (new guess).
Error = new guess - previous value = 847.7662134958 - 455.0827459632 = 392.6834675326.
392.6834675326 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 52900 by the previous result. d = 52900/455.0827459632 = 116.2425964712.
Average this value (d) with that of step 7: (116.2425964712 + 455.0827459632)/2 = 285.6626712172 (new guess).
Error = new guess - previous value = 455.0827459632 - 285.6626712172 = 169.420074746.
169.420074746 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 52900 by the previous result. d = 52900/285.6626712172 = 185.1834535279.
Average this value (d) with that of step 8: (185.1834535279 + 285.6626712172)/2 = 235.4230623726 (new guess).
Error = new guess - previous value = 285.6626712172 - 235.4230623726 = 50.2396088446.
50.2396088446 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 52900 by the previous result. d = 52900/235.4230623726 = 224.7018599914.
Average this value (d) with that of step 9: (224.7018599914 + 235.4230623726)/2 = 230.062461182 (new guess).
Error = new guess - previous value = 235.4230623726 - 230.062461182 = 5.3606011906.
5.3606011906 > 0.001. As error > accuracy, we repeat this step again.
Step 11:
Divide 52900 by the previous result. d = 52900/230.062461182 = 229.937555776.
Average this value (d) with that of step 10: (229.937555776 + 230.062461182)/2 = 230.000008479 (new guess).
Error = new guess - previous value = 230.062461182 - 230.000008479 = 0.062452703.
0.062452703 > 0.001. As error > accuracy, we repeat this step again.
Step 12:
Divide 52900 by the previous result. d = 52900/230.000008479 = 229.999991521.
Average this value (d) with that of step 11: (229.999991521 + 230.000008479)/2 = 230 (new guess).
Error = new guess - previous value = 230.000008479 - 230 = 0.000008479.
0.000008479 <= 0.001. As error <= accuracy, we stop the iterations and use 230 as the square root.
So, we can say that the square root of 52900 is 230 with an error smaller than 0.001 (in fact the error is 0.000008479). this means that the first 5 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(52900)' is 230.
Note: There are other ways to calculate square roots. This is only one of them.