The algorithm to find the square root of a natural number Square roots

The algorithm to find  the square root of a natural number.

To find  the square root of a natural number -using a piece of paper and a pencil- you have to take the following steps:

 Type a natural number (a radicand) in the window below and hit Enter. Next click on the triangles on the right to see the steps.
Esta unidad interactiva requiere la máquina virtual de Java J2RE.

1.- Mark groups of two digits in the radicand starting on the right.
2.- Calculate mentally the whole square root of the first group on the left, without exceeding it. Square that number and write down the result on the right.
3.- Subtract that square from the group of digits.
4.- If the subtraction is possible, move the number up into the root.
5.- Take down the next two digits from the radicand and place them on the right of the last remainder.
6.-Below, on the right, on a new line, write the double of the present root.
7. To calculate the next number of the root, take the number below on the left aside, ignore its last digit and then divide it by the number on the right.
8.- Put the number obtained together with the one below on the right and  multiply all that by that number. This product mustn't be larger than the number in the present remainder; if it is larger, try with one unit less in the digit.
9.- Write it on the left and subtract it.
10.-  If the subtraction is possible, take the number by which we have multiplied it up into the root.
11.- If the radicand has more groups of two digits, take down the next group   and continue the process in the same way right to the end.

 Eduardo Barbero Corral Spanish Ministry of Education. Year 2007