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 guessandcheck 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(162)
= sqrt{ 16 (1 2/16)} = 4 sqrt(1 1/8) use binomial theorem to expand (11/8) to the power 1/2 = 4 (11/16) higher powers of 1/8 may be neglected = 4  1/4 = 15/4 = 3. 750

It is 3.74165739
So rounded: 3.742