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Thanks very much, Litertly got itnah wrong.
2 * 2 * 2 * 5 * 7 * k = 280k
when we find the squre root of 2 * 2, itl be ofcourse a single 2.
the same way under-root ( 2* 2 * 2 * 2) = 2 * 2
and underoot (2 * 2 * 2 * 2 * 2 * 2) = 2 * 2 * 2
so if we have 2 * 2 * 2, u need to multiply it with such a number that the total number of 2's becomes even
like, 2 * 2 * 2 * 2 is a proper square root.
the same way underoot(2 * 2 * 2 * 2 * 2 * 2 * 3 * 3 * 11 * 11) = 2 * 2 * 2 * 3 * 11
got it?
so all u need to do is, make the number of all prime factors 'even'
280k = 2 * 2 * 2 * 5 * 7 * k
280 k = 2 * 2 * 2 * 2 * 5 * 5 * 7 * 7
so k = 2 * 5 * 7
but if we had 1400 instead of 280 in the Question. where prime factors of 1400 are 2 * 2 * 2 * 5 * 5 * 7
we only need to to increase the number of all the prime factors which is divisible by 2 (coz we have to find SQUARE root, and if we had to find cube root, we'll increase the number of prime factors so that 'that' number of each of the prime factors is divisible by 3)
so we will do it this way 1400k = 2 * 2 * 2 * 2 * 5 * 5 * 7 * 7
k = 2*7
got it?
So when we have to find k in perfect square, all we need to do is make PrimeFactorization even.......... and numbers we multiply them by ( to make even, are what we multiply to get answer)
In b) we will increase the numbers to get 3 time each.......... like for 882k
So the Prime factorization is : 2 * 5 * 5 * 7 * 7
So let make all prime factors divisible by 3: 2* 2* 2 * 5 * 5* 5* 7 * 7* 7
We have 2*2*5*7=84........ It looked easy but was beast
Thanks amd, see did I got it?