square root of 11580
Answers
Answer:
= 107.61
Step-by-step explanation:
√11580
=107.61
Answer:
√11580 = 107.61040841852
Step-by-step explanation:
Step 1:
Divide the number (11580) by 2 to get the first guess for the square root .
First guess = 11580/2 = 5790.
Step 2:
Divide 11580 by the previous result. d = 11580/5790 = 2.
Average this value (d) with that of step 1: (2 + 5790)/2 = 2896 (new guess).
Error = new guess - previous value = 5790 - 2896 = 2894.
2894 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 11580 by the previous result. d = 11580/2896 = 3.9986187845.
Average this value (d) with that of step 2: (3.9986187845 + 2896)/2 = 1449.9993093923 (new guess).
Error = new guess - previous value = 2896 - 1449.9993093923 = 1446.0006906077.
1446.0006906077 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 11580 by the previous result. d = 11580/1449.9993093923 = 7.9862107002.
Average this value (d) with that of step 3: (7.9862107002 + 1449.9993093923)/2 = 728.9927600462 (new guess).
Error = new guess - previous value = 1449.9993093923 - 728.9927600462 = 721.0065493461.
721.0065493461 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 11580 by the previous result. d = 11580/728.9927600462 = 15.8849314214.
Average this value (d) with that of step 4: (15.8849314214 + 728.9927600462)/2 = 372.4388457338 (new guess).
Error = new guess - previous value = 728.9927600462 - 372.4388457338 = 356.5539143124.
356.5539143124 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 11580 by the previous result. d = 11580/372.4388457338 = 31.0923528323.
Average this value (d) with that of step 5: (31.0923528323 + 372.4388457338)/2 = 201.7655992831 (new guess).
Error = new guess - previous value = 372.4388457338 - 201.7655992831 = 170.6732464507.
170.6732464507 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 11580 by the previous result. d = 11580/201.7655992831 = 57.393331872.
Average this value (d) with that of step 6: (57.393331872 + 201.7655992831)/2 = 129.5794655776 (new guess).
Error = new guess - previous value = 201.7655992831 - 129.5794655776 = 72.1861337055.
72.1861337055 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 11580 by the previous result. d = 11580/129.5794655776 = 89.3660114153.
Average this value (d) with that of step 7: (89.3660114153 + 129.5794655776)/2 = 109.4727384964 (new guess).
Error = new guess - previous value = 129.5794655776 - 109.4727384964 = 20.1067270812.
20.1067270812 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 11580 by the previous result. d = 11580/109.4727384964 = 105.7797599571.
Average this value (d) with that of step 8: (105.7797599571 + 109.4727384964)/2 = 107.6262492267 (new guess).
Error = new guess - previous value = 109.4727384964 - 107.6262492267 = 1.8464892697.
1.8464892697 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 11580 by the previous result. d = 11580/107.6262492267 = 107.5945699418.
Average this value (d) with that of step 9: (107.5945699418 + 107.6262492267)/2 = 107.6104095842 (new guess).
Error = new guess - previous value = 107.6262492267 - 107.6104095842 = 0.0158396425.
0.0158396425 > 0.001. As error > accuracy, we repeat this step again.
Step 11:
Divide 11580 by the previous result. d = 11580/107.6104095842 = 107.6104072528.
Average this value (d) with that of step 10: (107.6104072528 + 107.6104095842)/2 = 107.6104084185 (new guess).
Error = new guess - previous value = 107.6104095842 - 107.6104084185 = 0.0000011657.
0.0000011657 <= 0.001. As error <= accuracy, we stop the iterations and use 107.6104084185 as the square root