SOLUTION: I need to know how to solve a problem. I no the answer but i dont no how to expain. the prolem shows a tiny 3 almost ontop of the square root symbol then the square root -243 which

Algebra ->  Square-cubic-other-roots -> SOLUTION: I need to know how to solve a problem. I no the answer but i dont no how to expain. the prolem shows a tiny 3 almost ontop of the square root symbol then the square root -243 which      Log On


   

Question 103991: I need to know how to solve a problem. I no the answer but i dont no how to expain. the prolem shows a tiny 3 almost ontop of the square root symbol then the square root -243 which i have to simlify. the answer is -6 but i dont no how to explain how i got my answer! please help me!!!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

root%283%2C-243%29 Start with the given expression


The goal of simplifying expressions with third roots is to factor the radicand into a product of two numbers.
One of these two numbers must be a value in which you can take the third root and still get a rational number.
So let's list the factors of -243
Factors:
1, 3, 9, 27, 81, 243


Notice how 27 is the largest value in which you can take the third root and still get a rational number, so lets break -243 down into -27*9


root%283%2C-27%2A9%29 Factor -243 into -27*9

root%283%2C-27%29%2Aroot%283%2C9%29 Break up the roots using the identity root%28n%2Cx%2Ay%29=root%28n%2Cx%29%2Aroot%28n%2Cy%29

-3%2Aroot%283%2C9%29 Take the third root of -27 to get -3