Question 190599
{{{2*root(3,16)-4*root(3,54)}}} Start with the given expression.



{{{2*root(3,8*2)-4*root(3,54)}}} Factor 16 to get {{{8*2}}}. Note: 8 is a perfect cube.



{{{2*root(3,8*2)-4*root(3,27*2)}}} Factor 54 to get {{{27*2}}}. Note: 27 is a perfect cube.



{{{2*root(3,8)*root(3,2)-4*root(3,27)*root(3,2)}}} Break up the roots.



{{{2*2*root(3,2)-4*3*root(3,2)}}} Take the cube root of 8 to get 2



{{{4*root(3,2)-12*root(3,2)}}} Take the cube root of 27 to get 3



{{{(4-12)*root(3,2)}}} Factor out the GCF {{{root(3,2)}}}



{{{-8*root(3,2)}}} Combine like terms.



So {{{2*root(3,16)-4*root(3,54)=-8*root(3,2)}}}