SOLUTION: Please help me solve this( To me, Complicated question) ! Your detailed explanation are very much appreciated! :D : Given that 441=3^2x7^2 and 1005=3x5x67, Find the smallest possi

Algebra ->  Square-cubic-other-roots -> SOLUTION: Please help me solve this( To me, Complicated question) ! Your detailed explanation are very much appreciated! :D : Given that 441=3^2x7^2 and 1005=3x5x67, Find the smallest possi      Log On


   

Question 938361: Please help me solve this( To me, Complicated question) ! Your detailed explanation are very much appreciated! :D :
Given that 441=3^2x7^2 and 1005=3x5x67, Find the smallest possible whole number K for which
A) 1005k x 441 is a perfect square
B) 1005 X 441K is a perfect cube
My working:
a) (3 x 5 x 67)k x (3^2x7^2) = (3x3 ^2x7^2x5x67)k
=(3^3 x 7^2x5x67) k
And then I'm stuck...... Please hhelp as soon as possible!! Keep on thinking hard but still cant solve D:

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1005k%2A441=3%2A5%2A67%2Ak%2A3%5E2%2A7%5E2=3%5E3%2A5%2A67%2Ak
For it to be a perfect square, all the factors need to have a exponent that is a multiple of 2.
k=3%2A5%2A67
k=1005
.
.
.
For the factors to be cubed, the exponents must be multiples of 3.
1005k%2A441=3%2A5%2A67%2Ak%2A3%5E2%2A7%5E2=3%5E3%2A5%2A7%5E2%2A67%2Ak
3 is already a multiple.
5 needs 5%5E2
7 needs 7
67 needs 67%5E2
k=5%5E2%2A7%2A67%5E2
k=785575