SOLUTION: How do I factor a radicand to the perfect fourth power? I have the problem. 4√486x^12y^14. I know that it becomes 4√81*6*x^12y^14 and the answer is 3x^3y^34√6y^2.

Algebra ->  Square-cubic-other-roots -> SOLUTION: How do I factor a radicand to the perfect fourth power? I have the problem. 4√486x^12y^14. I know that it becomes 4√81*6*x^12y^14 and the answer is 3x^3y^34√6y^2.      Log On


   

Question 628207: How do I factor a radicand to the perfect fourth power? I have the problem. 4√486x^12y^14. I know that it becomes 4√81*6*x^12y^14 and the answer is 3x^3y^34√6y^2. I am having trouble understanding how 486 became 81 and then 3x. your help would be greatly appreciated.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
the problem. 4sqrt%28486x%5E12y%5E14%29
factor in a manner that will will reveal the perfect 4th power values
4th power of 3 is 81 and is also a factor of 486, going into that 6 times
:
4sqrt%2881%2A6%2Ax%5E4%2Ax%5E4%2Ax%5E4%2Ay%5E4%2Ay%5E4%2Ay%5E2%29
extract the 4th root of the perfect 4ths and you have
3*x*x*x*y*y*4sqrt%286y%5E2%29
which is
3x%5E3%2Ay%5E24sqrt%286y%5E2%29