Question 103966
{{{8*root(3,16)}}} 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 16

Factors:

1, 2, 4, 8, 16



Notice how 8 is the largest value in which you can take the third root and still get a rational number, so lets break 16 down into 8*2



{{{8*root(3,8*2)}}} Factor 16 into 8*2
 
{{{8*root(3,8)*root(3,2)}}} Break up the roots using the identity {{{root(n,x*y)=root(n,x)*root(n,y)}}}
 
{{{8*2*root(3,2)}}} Take the third root of 8 to get 2 



{{{16*root(3,2)}}} Multiply