You have a correct solution here, but the calculations would be made a lot easier if you solved first for "d". Assuming that no calculators are allowed, there is still a simple way to solve the equation : d^2 = 1002001 ( and I'm pretty sure that this is what the proposers of this problem intended ). Notice that the pattern in this number looks quite clearly like the binomial expansion of ( x + 1 )^2 = x^2 + 2x + 1 with "x" = 1000. Therefore, (1000 + 1) ^2 = 1,000^2 + 2(1)(1000) + 1^2 = 1,000,000 + 2000 + 1 = 1002001 . Therefore : sqrt ( 1002001 ) = 1001 = (7)(11)(13), and the problem is quickly solved from there : a = 8(1001)/ (7)(11)(13) = 8 ; therefore, a^2 = 64.
You have a correct solution here, but the calculations would be made a lot easier if you solved first for "d". Assuming that no calculators are allowed, there is still a simple way to solve the equation : d^2 = 1002001 ( and I'm pretty sure that this is what the proposers of this problem intended ). Notice that the pattern in this number looks quite clearly like the binomial expansion of ( x + 1 )^2 = x^2 + 2x + 1 with "x" = 1000. Therefore, (1000 + 1) ^2 = 1,000^2 + 2(1)(1000) + 1^2 = 1,000,000 + 2000 + 1 = 1002001 . Therefore : sqrt ( 1002001 ) = 1001 = (7)(11)(13), and the problem is quickly solved from there : a = 8(1001)/ (7)(11)(13) = 8 ; therefore, a^2 = 64.
🙂