Examples


Here are some examples to make the steps clearer:

Example 1: Approximate .

  1. 25 is close to 22. = 5
  2. 22/5 = 4.4
  3. (5 + 4.4)/2 = 4.7
  4. 22/4.7 = 4.68
  5. (4.7 + 4.68)/2 = 4.69
  6. 22/4.69 = 4.69
= 4.69

Example 2: Approximate .

  1. 71 is close to 64. = 8
  2. 71/8 = 8.9
  3. (8 + 8.9)/2 = 8.45
  4. 71/8.45 = 8.40
  5. (8.45 + 8.40)/2 = 8.425
  6. 71/8.425 = 8.427
  7. (8.425 + 8.427)/2 = 8.426
  8. 71/8.426 = 8.426
= 8.426

Example 3: Approximate .
can be simplified: = = 2× = 2×
Approximate :
  1. 14 is close to 16. = 4
  2. 14/4 = 3.5
  3. (4 + 3.5)/2 = 3.75
  4. 14/3.75 = 3.73
  5. (3.75 + 3.73)/2 = 3.74
  6. 14/3.74 = 3.74
= 3.74

Thus, = 2× = 2×3.74 = 7.48

Note that the eventual result will be the same no matter what perfect square one picks in Step 1.