History of Hindu Mathematics: A Source Book v1.c8.s10.3

v1.c8.s10.3

"Add together the own digits of the numbers forming the multiplicand, multiplier, and product upto one place;² such should be done with the dividend, divisor, quotient and remainder, etc. Then if the number (of one digit) obtained from the product of those numbers (that have been already obtained) from the multiplicand and the multiplier be equal to that obtained from the product, the multiplication is true. If the number, which results from the product of those obtained from the quotient and the divisor, added to that from the remainder, be equal to that obtained from the dividend, the division is true. Add together the digits of a number, its (nearest) square-root (in integers) and of the remainder. If the number, obtained from the square of that (number) which is obtained from the square-root plus the number obtained from the remainder, be equal to that which results from the given number, the root-extraction is true. If the number, resulting from the cube of the number obtained by adding the digits of the cube-root plus the number obtained from the remainder, be equal to the number resulting from the given number, then the operation is correct. Such are the easy tests for correctness of multiplication etc."