The smallest number which can be multiplied by 560 to give a cubic number is 2^2 x a^2 x b^c. find the values of a,b and c.
Thanks in advance. (:
560 = 2^4 * 5 * 7
for a cubic number, the smallest number that can be multiplied is
2^2 * 5^2 * 7^2
so that we will get 2^6 * 5^3 * 7^3 in the end, which is a cubic number
Hence,
a = 5, b =7 and c = 2
Regards,
Eagle
ExamWorld
Strategic Tuition
Originally posted by eagle:560 = 2^4 * 5 * 7
for a cubic number, the smallest number that can be multiplied is
2^2 * 5^2 * 7^2so that we will get 2^6 * 5^3 * 7^3 in the end, which is a cubic number
Hence,
a = 5, b =7 and c = 2
Regards,
Eagle
ExamWorld
Strategic Tuition
wa power ar u,so fast reply liao! thanks anyway! :D
wait..hmm i dont understand what u doing at all (((X
splitting it up into it's prime numbers
because
2^3 is a cubic number
2^6 is also a cubic number
5^3 and 7^3 are both cubic numbers
so 2^6 * 5^3 * 7^3 is also cubic number
so, since 560 = 2^4 * 5 * 7, obviously, we need to multiply 2^2 * 5^2 * 7^2 at the very least to make it 2^6 * 5^3 * 7^3, so that it becomes a cubic number.
\: but i still dont get why c=2..
because the smallest number we need to multiply into 560 to make it cubic is
2^2 * 5^2 * 7^2
so when compared to 2^2 x a^2 x b^c
a = 5, b = 7 and c = 2
Originally posted by eagle:because the smallest number we need to multiply into 560 to make it cubic is
2^2 * 5^2 * 7^2
so when compared to 2^2 x a^2 x b^c
a = 5, b = 7 and c = 2
oh i see...nabei so clever,u teacher or what? o_o
Originally posted by Maith:oh i see...nabei so clever,u teacher or what? o_o
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i see..thanks anyway for being so patient :D
no problem
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