square root of 14 rounded to the nearest thousandths?

NetherCraft 0

4 Answers

  • sqrt(14) = 3.74165739

    Rounded to the nearest thousandths, that is 3.742.

    Or do you want to know a manual algorithm for calculating square roots to the third decimal point (thousandths) level of accuracy? If so, look at Babylonian method or guess-and-check or other methods, see this site for easy to understand explanations and alternative algorithms:

    www.homeschoolmath.net

  • sqrt 14=3.7416574 or 3.742 to nearest thousandth

  • sqrt(14)=sqrt(16-2)

          = sqrt{ 16 (1- 2/16)}
    
          = 4 sqrt(1- 1/8) use binomial theorem to expand (1-1/8) to the power 1/2 
    
          = 4 (1-1/16)  higher powers of 1/8 may be neglected 
    
          = 4 - 1/4
    
          = 15/4
    
          = 3. 750
  • It is 3.74165739

    So rounded: 3.742

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