square root of 956 by long division method
Answers
Answer:
square root of 956 is 30.9192496675
Answer:
The square root of 956 with one digit decimal accuracy is 30.9.
Step-by-step explanation:
Step 1:
Divide the number (956) by 2 to get the first guess for the square root .
First guess = 956/2 = 478.
Step 2:
Divide 956 by the previous result. d = 956/478 = 2.
Average this value (d) with that of step 1: (2 + 478)/2 = 240 (new guess).
Error = new guess - previous value = 478 - 240 = 238.
238 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 956 by the previous result. d = 956/240 = 3.9833333333.
Average this value (d) with that of step 2: (3.9833333333 + 240)/2 = 121.9916666667 (new guess).
Error = new guess - previous value = 240 - 121.9916666667 = 118.0083333333.
118.0083333333 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 956 by the previous result. d = 956/121.9916666667 = 7.8366008607.
Average this value (d) with that of step 3: (7.8366008607 + 121.9916666667)/2 = 64.9141337637 (new guess).
Error = new guess - previous value = 121.9916666667 - 64.9141337637 = 57.077532903.
57.077532903 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 956 by the previous result. d = 956/64.9141337637 = 14.7271471492.
Average this value (d) with that of step 4: (14.7271471492 + 64.9141337637)/2 = 39.8206404564 (new guess).
Error = new guess - previous value = 64.9141337637 - 39.8206404564 = 25.0934933073.
25.0934933073 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 956 by the previous result. d = 956/39.8206404564 = 24.0076500288.
Average this value (d) with that of step 5: (24.0076500288 + 39.8206404564)/2 = 31.9141452426 (new guess).
Error = new guess - previous value = 39.8206404564 - 31.9141452426 = 7.9064952138.
7.9064952138 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 956 by the previous result. d = 956/31.9141452426 = 29.9553690921.
Average this value (d) with that of step 6: (29.9553690921 + 31.9141452426)/2 = 30.9347571674 (new guess).
Error = new guess - previous value = 31.9141452426 - 30.9347571674 = 0.9793880752.
0.9793880752 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 956 by the previous result. d = 956/30.9347571674 = 30.9037499414.
Average this value (d) with that of step 7: (30.9037499414 + 30.9347571674)/2 = 30.9192535544 (new guess).
Error = new guess - previous value = 30.9347571674 - 30.9192535544 = 0.015503613.
0.015503613 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 956 by the previous result. d = 956/30.9192535544 = 30.9192457806.
Average this value (d) with that of step 8: (30.9192457806 + 30.9192535544)/2 = 30.9192496675 (new guess).
Error = new guess - previous value = 30.9192535544 - 30.9192496675 = 0.0000038869.
0.0000038869 <= 0.001. As error <= accuracy, we stop the iterations and use 30.9192496675 as the square root.
So, we can say that the square root of 956 is 30.91924 with an error smaller than 0.001 (in fact the error is 0.0000038869). this means that the first 5 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(956)' is 30.919249667480614.