find the square root of 2,70,400with method of prime factorisration ( class 8th ch squares and square root) I need full explation ans please
Answers
Answer:
520
Step-by-step explanation:
Step 1:
Divide the number (270400) by 2 to get the first guess for the square root .
First guess = 270400/2 = 135200.
Step 2:
Divide 270400 by the previous result. d = 270400/135200 = 2.
Average this value (d) with that of step 1: (2 + 135200)/2 = 67601 (new guess).
Error = new guess - previous value = 135200 - 67601 = 67599.
67599 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 270400 by the previous result. d = 270400/67601 = 3.9999408293.
Average this value (d) with that of step 2: (3.9999408293 + 67601)/2 = 33802.4999704146 (new guess).
Error = new guess - previous value = 67601 - 33802.4999704146 = 33798.5000295854.
33798.5000295854 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 270400 by the previous result. d = 270400/33802.4999704146 = 7.9994083348.
Average this value (d) with that of step 3: (7.9994083348 + 33802.4999704146)/2 = 16905.2496893747 (new guess).
Error = new guess - previous value = 33802.4999704146 - 16905.2496893747 = 16897.2502810399.
16897.2502810399 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 270400 by the previous result. d = 270400/16905.2496893747 = 15.9950314233.
Average this value (d) with that of step 4: (15.9950314233 + 16905.2496893747)/2 = 8460.622360399 (new guess).
Error = new guess - previous value = 16905.2496893747 - 8460.622360399 = 8444.6273289757.
8444.6273289757 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 270400 by the previous result. d = 270400/8460.622360399 = 31.9598238146.
Average this value (d) with that of step 5: (31.9598238146 + 8460.622360399)/2 = 4246.2910921068 (new guess).
Error = new guess - previous value = 8460.622360399 - 4246.2910921068 = 4214.3312682922.
4214.3312682922 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 270400 by the previous result. d = 270400/4246.2910921068 = 63.6791011579.
Average this value (d) with that of step 6: (63.6791011579 + 4246.2910921068)/2 = 2154.9850966323 (new guess).
Error = new guess - previous value = 4246.2910921068 - 2154.9850966323 = 2091.3059954745.
2091.3059954745 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 270400 by the previous result. d = 270400/2154.9850966323 = 125.4765058109.
Average this value (d) with that of step 7: (125.4765058109 + 2154.9850966323)/2 = 1140.2308012216 (new guess).
Error = new guess - previous value = 2154.9850966323 - 1140.2308012216 = 1014.7542954107.
1014.7542954107 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 270400 by the previous result. d = 270400/1140.2308012216 = 237.1449707465.
Average this value (d) with that of step 8: (237.1449707465 + 1140.2308012216)/2 = 688.687885984 (new guess).
Error = new guess - previous value = 1140.2308012216 - 688.687885984 = 451.5429152376.
451.5429152376 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 270400 by the previous result. d = 270400/688.687885984 = 392.6306901909.
Average this value (d) with that of step 9: (392.6306901909 + 688.687885984)/2 = 540.6592880875 (new guess).
Error = new guess - previous value = 688.687885984 - 540.6592880875 = 148.0285978965.
148.0285978965 > 0.001. As error > accuracy, we repeat this step again.
Step 11:
Divide 270400 by the previous result. d = 270400/540.6592880875 = 500.1301299317.
Average this value (d) with that of step 10: (500.1301299317 + 540.6592880875)/2 = 520.3947090096 (new guess).
Error = new guess - previous value = 540.6592880875 - 520.3947090096 = 20.2645790779.
20.2645790779 > 0.001. As error > accuracy, we repeat this step again.
Step 12:
Divide 270400 by the previous result. d = 270400/520.3947090096 = 519.6055903693.
Average this value (d) with that of step 11: (519.6055903693 + 520.3947090096)/2 = 520.0001496894 (new guess).
Error = new guess - previous value = 520.3947090096 - 520.0001496894 = 0.3945593202.
0.3945593202 > 0.001. As error > accuracy, we repeat this step again.
Step 13:
Divide 270400 by the previous result. d = 270400/520.0001496894 = 519.9998503106.
Average this value (d) with that of step 12: (519.9998503106 + 520.0001496894)/2 = 520 (new guess).
Error = new guess - previous value = 520.0001496894 - 520 = 0.0001496894.
0.0001496894 <= 0.001. As error <= accuracy, we stop the iterations and use 520 as the square root.
Answer:
in this solution your answer is fully explained
