Question 509587: how do you get 9.43 from the square root of 89
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
You don't. Saying  is incorrect. In fact, saying  , which is the answer the built-in Windows calculator gives, is also incorrect. Both are approximations, although one is much closer than the other. Since  is an irrational number it is impossible to write it exactly as a decimal fraction. On the other hand, 9.43 is probably close enough for most purposes.
Just looking at and not having a calculator, one way to go about it is to recognize that  and  , and since  ,  . Then 89 is a little less than half-way from 81 to 100, so if you try 9.5 times 9.5 to get 90.25 (too big) and 9.4 times 9.4 to get 88.36 (too small), you know you have to be somewhere in between. Keep refining to as many decimal points as you like.
John
My calculator said it, I believe it, that settles it
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