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anonymous
 one year ago
If K is an integer, what is the smallest possible value of K such that 1040K is the square of an integer?
anonymous
 one year ago
If K is an integer, what is the smallest possible value of K such that 1040K is the square of an integer?

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taramgrant0543664
 one year ago
Best ResponseYou've already chosen the best response.01040k = 2*2*2*2*5*13*k to make it a square: (2*2*5*13) (2*2 *k) so k must= 5* 13 or 65

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait im not understanding this problem can you explain in details? in other words dumb it down for me

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0honestly i dont even know what theyre asking for

taramgrant0543664
 one year ago
Best ResponseYou've already chosen the best response.0I don't really know how to explain it very well, you have to break it into its counterparts as the prime factors

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0why is it 65 why muktiply 13 *5

taramgrant0543664
 one year ago
Best ResponseYou've already chosen the best response.0Because the 2's have counterparts but the 5 and the 13 doesn't so you can multiply them together

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so we're looking for the product without duplicate numbers?

taramgrant0543664
 one year ago
Best ResponseYou've already chosen the best response.0The numbers 5 and 13 can't break down any farther without becoming an irrational number

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so what if there was 2x2x2x2x3x3x5x7x8?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then is it 2^2 and 3^3 and 5x7x8?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0just multiply the last 3?

taramgrant0543664
 one year ago
Best ResponseYou've already chosen the best response.0You divide by 2 initially as it is the smallest integer so that's why you have 2^4, at that point you can't divide be two anymore without it becoming a rational number because you are left at 65. 3 and 4 don't divide into that so the next real number that divides into it is 5 so that's why you get 5 and 13 and neither of those can be broken down anymore

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you break down the question for me cuz i dont understand the last part of the question... "such that 1040K is the square of an integer?" What does this mean?

taramgrant0543664
 one year ago
Best ResponseYou've already chosen the best response.0We need to find a number k such that 1040k = 2^n for some number n. The prime factorization of 1040 is 2^4 5^1 13^1. In order for 1040k to be a square number, we need every prime factor in 1040k to be at least raised to the second power. The only numbers that are not are 5 and 13  thus, we need one more factor of 5 and one more factor of 13. Therefore, k = 5*13 = 65.
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