by 
Kitty
ANSWERS: 1
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My dad taught me how to do square roots 15.000000 nearest square = 3*3=9 So first digit of the result is 3. subtract the 9 to give 6.000000 Double the current result: 6. now search for a digit d with 6.d * .d = 6.00 d = 8 works closest: 6.8 * .8 = 5.44 This is the next digit of the answer. The answer is now: 3.8 Subtract the 5.44 to give 0.560000 Double the current result = 7.6 Look for a digit d with 7.6d * 0.0d = 0.5600 d = 7 works closest: 7.67 * 0.07 = 0.5369 The answer is now: 3.87 Subtract the 0.5369 to give 0.023100 Double the current result = 7.74 Look for a digit d with 7.74d = 0.00d = 0.023100 somehere between 2 and 3. 7.742 * 0.002 = 0.015484 7.743 * 0.003 = 0.023229 3 is closest. The answer is now 3.873 to the nearest thousandth Alternative method based on Netwon's method: Guess the answer: 3 Divide into 15: 5 take the average of 3 and 5: 4 Divide into 15: 3.75 take the average of 4 and 3.75 = 3.875 (31/8) Divide into 15: 3.87096 (120/31) take the average: 3.87298 (1921/496) Divide into 15: 3.87298 (7440/1921) Each pair brackets the solution, so we must have the answer to the nearest thousandth: 3.873
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