Question 103991


{{{root(3,-243)}}} 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(3,-27*9)}}} Factor -243 into -27*9
 
{{{root(3,-27)*root(3,9)}}} Break up the roots using the identity {{{root(n,x*y)=root(n,x)*root(n,y)}}}
 
{{{-3*root(3,9)}}} Take the third root of -27 to get -3