Question 190603
{{{sqrt(18m^3)-sqrt(72m^3)}}} Start with the given expression.



{{{sqrt(9*2*m^2*m)-sqrt(36*2*m^2*m)}}} Factor 



Note: {{{18m^3}}} factors to {{{9*2*m^2*m}}} and {{{72m^3}}} factors to {{{36*2*m^2*m}}}


{{{sqrt(9)*sqrt(2)*sqrt(m^2)*sqrt(m)-sqrt(36)*sqrt(2)*sqrt(m^2)*sqrt(m)}}} Break up the square roots.



{{{3*sqrt(2)*m*sqrt(m)-6*sqrt(2)*m*sqrt(m)}}} Take the square root of 9, 36, and {{{m^2}}} to get 3, 6, and "m" respectively



{{{3m*sqrt(2m)-6m*sqrt(2m)}}} Multiply and recombine the roots.



{{{(3m-6m)*sqrt(2m)}}} Factor out the GCF {{{sqrt(2m)}}}



{{{-3m*sqrt(2m)}}} Combine like terms.



So {{{sqrt(18m^3)-sqrt(72m^3)=-3m*sqrt(2m)}}} where {{{m>=0}}}