Square root

To find the square root of a decimal fraction (for example, $65432.109$), start by dividing the number into groups of two digits each, both to the left and right of the decimal point. The leftmost group may contain just one digit (e.g., $6$). Identify the first digit of the square root ($2$) as the largest digit whose square does not exceed the first group ($6$). Subtract the square of this digit ($4$) from the first group, and append the next group ($54$) to the right of the result. To the left of this new number ($254$), write twice the first digit of the root ($4$), and choose the next digit ($5$) as the largest digit whose product with the number formed by appending it to the doubled first digit (45 \cdot 5 = 225) does not exceed the current number ($254$). This digit ($5$) is then added to the root, and the process continues. The decimal point in the root is placed when the first group to the right of the decimal point is appended.

Write a program that computes the square root of a positive decimal fraction.