1. 1000-457

(9-4)(9-5)(10-7) = 543

 2. 1000-54 = 1000-054 = (9-0)(9-5)(10-4) = 946

Corollary: Yavdunam Jaavdunikritya Varga Yojayet or "Whatever the extent of its deficiency, lessen it still further to that very extend; and also setup the square of thet deficiency."

 3. computing square of 8

power of 10 nearest to 8 is 10, so take 10 as base

8 is 2 less than 10 so 8-2 or 6 is the left side of the answer

right hand side of the answer is square of 2(deficiency) i.e., 4

so the answer is 64

 

similarly square of 7 is (7-3) (3x3) = 49

 

** if the number is greater than 10 take the surplus

 

square of 12 is (12+2) (2x2) = 144

square of 13 is (13+3) (3x3) = 169