find √9.4 using long division method
Answers
Answer:
3.0695
Step-by-step explanation:
Step 1:
Divide the number (9.4) by 2 to get the first guess for the square root .
First guess = 9.4/2 = 4.7.
Step 2:
Divide 9.4 by the previous result. d = 9.4/4.7 = 2.
Average this value (d) with that of step 1: (2 + 4.7)/2 = 3.35 (new guess).
Error = new guess - previous value = 4.7 - 3.35 = 1.35.
1.35 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 9.4 by the previous result. d = 9.4/3.35 = 2.8059701493.
Average this value (d) with that of step 2: (2.8059701493 + 3.35)/2 = 3.0779850747 (new guess).
Error = new guess - previous value = 3.35 - 3.0779850747 = 0.2720149253.
0.2720149253 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 9.4 by the previous result. d = 9.4/3.0779850747 = 3.0539459328.
Average this value (d) with that of step 3: (3.0539459328 + 3.0779850747)/2 = 3.0659655038 (new guess).
Error = new guess - previous value = 3.0779850747 - 3.0659655038 = 0.0120195709.
0.0120195709 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 9.4 by the previous result. d = 9.4/3.0659655038 = 3.0659183831.
Average this value (d) with that of step 4: (3.0659183831 + 3.0659655038)/2 = 3.0659419435 (new guess).
Error = new guess - previous value = 3.0659655038 - 3.0659419435 = 0.0000235603.
0.0000235603 <= 0.001. As error <= accuracy, we stop the iterations and use 3.0659419435 as the square root.
So, we can say that the square root of 9.4 is 3.0659 with an error smaller than 0.001 (in fact the error is 0.0000235603). this means that the first 4 decimal places are correct.
Hope it helped you
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