The algorithm of the square root with decimal digits
Square roots

The algorithm of the square root with decimal digits.

Only the natural numbers that are square perfects have another natural number as a square root. In the rest of the cases, in order to find its square root more accurately and exactly, you have to get decimal digits.
To work out the square root with decimal digits we follow the same method as for natural numbers, with a slight modification:

Esta unidad interactiva requiere la máquina virtual de Java J2RE.

Type a decimal number in the control box below (remember that you have to use a dot instead of a comma to separate the whole part from the decimal part).

- Groups of two digits are marked counting from the decimal point, in the whole part and the decimal part.

- The square root of the whole part is obtained by following the same steps as if it was a natural number.
If no more accuracy is required, you can consider the operation finished, but you can go on if more accuracy is required.

- When the whole part is finished, write a decimal point  in the root.

- The next two decimal digits are taken down.
If the radicand does not have decimal digits or it only has one digit, you have to write zeros until you get two digits.

- You follow the same method as if it was a whole part.

- We consider the operation finished when the number of decimal digits is the desired result or when all the decimal digits have been taken down and the remainder is zero.

  Eduardo Barbero Corral
Spanish Ministry of Education. Year 2007

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