Question

How to find square root of 53.64 ( full method)

Answer 1

Step 1: 
 Divide the number (53.64) by 2 to get the first guess for the square root.
 First guess = 53.64/2 = 26.82.Step 2:
 Divide 53.64 by the previous result. d = 53.64/26.82 = 2.
 Average this value (d) with that of step 1: (2 + 26.82)/2 = 14.41 (new guess).
 Error = new guess - previous value = 26.82 - 14.41 = 12.41.
 12.41 > 0.001. As error > accuracy, we repeat this step again.Step 3:
 Divide 53.64 by the previous result. d = 53.64/14.41 = 3.7224149896.
 Average this value (d) with that of step 2: (3.7224149896 + 14.41)/2 = 9.0662074948 (new guess).
 Error = new guess - previous value = 14.41 - 9.0662074948 = 5.3437925052.
 5.3437925052 > 0.001. As error > accuracy, we repeat this step again.Step 4:
 Divide 53.64 by the previous result. d = 53.64/9.0662074948 = 5.9164761043.
 Average this value (d) with that of step 3: (5.9164761043 + 9.0662074948)/2 = 7.4913417996 (new guess).
 Error = new guess - previous value = 9.0662074948 - 7.4913417996 = 1.5748656952.
 1.5748656952 > 0.001. As error > accuracy, we repeat this step again.Step 5:
 Divide 53.64 by the previous result. d = 53.64/7.4913417996 = 7.1602660024.
 Average this value (d) with that of step 4: (7.1602660024 + 7.4913417996)/2 = 7.325803901 (new guess).
 Error = new guess - previous value = 7.4913417996 - 7.325803901 = 0.1655378986.
 0.1655378986 > 0.001. As error > accuracy, we repeat this step again.Step 6:
 Divide 53.64 by the previous result. d = 53.64/7.325803901 = 7.3220633155.
 Average this value (d) with that of step 5: (7.3220633155 + 7.325803901)/2 = 7.3239336083 (new guess).
 Error = new guess - previous value = 7.325803901 - 7.3239336083 = 0.0018702927.
 0.0018702927 > 0.001. As error > accuracy, we repeat this step again.Step 7:
 Divide 53.64 by the previous result. d = 53.64/7.3239336083 = 7.3239331306.
 Average this value (d) with that of step 6: (7.3239331306 + 7.3239336083)/2 = 7.3239333695 (new guess).
 Error = new guess - previous value = 7.3239336083 - 7.3239333695 = 2.388e-7.
 2.388e-7 <= 0.001. As error <= accuracy, we stop the iterations and use 7.3239333695 as the square root.

Answer 2

open calculatoe nd type 53.64*53.64......simple