How do you find the square root of 85?

How do you find the square root of 85?

                                  <mathjax>%sqrt85%</mathjax> is a non-terminating, non-repeating decimal.   You cant finish finding it. <br></br>But you can get better and better approximations by: start with a number whose square is close to 85.   (9 or 10.   <mathjax>%9^2%</mathjax> is closer, so start there. Now divide 85 by <mathjax>%9%</mathjax> to get <mathjax>%9. 4444%</mathjax>  (to 4 places)<br></br>Average the two numbers <mathjax>%9%</mathjax> and <mathjax>%9. 4444%</mathjax><br></br><mathjax>%(9+9. 4444)/2=9. 2222%</mathjax>Repeat:<br></br><mathjax>%85-:9. 2222=9. 2169%</mathjax>  (rounded to 4 places)<br></br>Average: <mathjax>%(9. 2222+9. 2169)/2=9. 2196%</mathjax>Repeat:<br></br><mathjax>%85-:9. 2196=9. 2195%</mathjax>  (rounded to 4 places)<br></br>Average:  <mathjax>%(9. 2196+9. 2195)/2=9. 2196%</mathjax><mathjax>%sqrt85~~9. 2196%</mathjax>That answer is accurate to 4 decimal places.   If you need more accuracy, keep more decimal places at each step.