+1694 @EinsteinJr:/ I used that site to refresh my memory; I've learned that stuff some 50 years ago but have never used it since.
@Melody:/ It only seems complicated, but it is not. After you went through all the steps, you'll be able to do it. It is fun!
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| Square the 2, giving 4, write that underneath the 6, and subtract. Bring down the next pair of digits. | Then double the number above the square root symbol line (highlighted), and write it down in parenthesis with an empty line next to it as shown. | Next think what single-digit number something could go on the empty line so that forty-something times somethingwould be less than or equal to 245. 45 x 5 = 225 46 x 6 = 276, so 5 works. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Write 5 on top of line. Calculate 5 x 45, write that below 245, subtract, bring down the next pair of digits (in this case the decimal digits 00). | Then double the number above the line (25), and write the doubled number (50) in parenthesis with an empty line next to it as indicated: | Think what single digit numbersomething could go on the empty line so that five hundred-something times somethingwould be less than or equal to 2000. 503 x 3 = 1509 504 x 4 = 2016, so 3 works. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Calculate 3 x 503, write that below 2000, subtract, bring down the next digits. | Then double the 'number' 253 which is above the line (ignoring the decimal point), and write the doubled number 506 in parenthesis with an empty line next to it as indicated: | 5068 x 8 = 40544 5069 x 9 = 45621, which is less than 49100, so 9 works. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Thus to one decimal place, √645 = 25.4
+118677 I do not understand what you have done here civonamzuk. 
Do you know if there is a you tube clip or something to explain it available?
+870 I found an algorithm to determinate the Square roots without a calculator: http://www.homeschoolmath.net/teaching/square-root-algorithm.php
+118677 thank you EJ 
That is quite complicated. I am glad I have a trusty calculator LOL
+1694 @EinsteinJr:/ I used that site to refresh my memory; I've learned that stuff some 50 years ago but have never used it since.
@Melody:/ It only seems complicated, but it is not. After you went through all the steps, you'll be able to do it. It is fun!
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| Square the 2, giving 4, write that underneath the 6, and subtract. Bring down the next pair of digits. | Then double the number above the square root symbol line (highlighted), and write it down in parenthesis with an empty line next to it as shown. | Next think what single-digit number something could go on the empty line so that forty-something times somethingwould be less than or equal to 245. 45 x 5 = 225 46 x 6 = 276, so 5 works. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Write 5 on top of line. Calculate 5 x 45, write that below 245, subtract, bring down the next pair of digits (in this case the decimal digits 00). | Then double the number above the line (25), and write the doubled number (50) in parenthesis with an empty line next to it as indicated: | Think what single digit numbersomething could go on the empty line so that five hundred-something times somethingwould be less than or equal to 2000. 503 x 3 = 1509 504 x 4 = 2016, so 3 works. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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| Calculate 3 x 503, write that below 2000, subtract, bring down the next digits. | Then double the 'number' 253 which is above the line (ignoring the decimal point), and write the doubled number 506 in parenthesis with an empty line next to it as indicated: | 5068 x 8 = 40544 5069 x 9 = 45621, which is less than 49100, so 9 works. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Thus to one decimal place, √645 = 25.4
