To find the least possible number of square stones required to pave the courtyard, we need to calculate the area of the courtyard and then divide it by the area of a square stone.
The length of the courtyard is given as 57 m 50 cm, which is equal to 57.5 meters. The breadth of the courtyard is given as 22 meters.
To find the area of the courtyard, we use the formula: Area = Length x Breadth.
Therefore, the area of the courtyard is 57.5 meters x 22 meters = 1265 square meters.
Now, let's assume the size of each square stone is "x" meters.
The area of one square stone is equal to "x" meters x "x" meters = x^2 square meters.
Now, to find the number of square stones required, we divide the area of the courtyard by the area of one square stone:
Number of square stones = Area of courtyard / Area of one square stone
Number of square stones = 1265 square meters / x^2 square meters
Since we want to find the least possible number of square stones required, we need to find the largest perfect square number that is less than or equal to 1265.
1265 is between the squares of 35 and 36. The square of 35 is 1225, and the square of 36 is 1296.
Therefore, the largest perfect square number that is less than or equal to 1265 is 1225.
Plugging this value back into the equation:
Number of square stones = 1265 square meters / 1225 square meters
Number of square stones = 1.03469...
Since we can't have a fraction of a square stone, we need to round up to the nearest whole number. Therefore, the least possible number of square stones required to pave the courtyard is 2.