Question 599069


{{{sqrt(200*m^4*n)}}} Start with the given expression.



{{{sqrt(100*2*m^4*n)}}} Factor {{{200}}} into {{{100*2}}}



{{{sqrt(100*2*m^2*m^2*n)}}} Factor {{{m^4}}} into {{{m^2*m^2}}}



{{{sqrt(100)*sqrt(2)*sqrt(m^2)*sqrt(m^2)*sqrt(n)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{10*sqrt(2)*sqrt(m^2)*sqrt(m^2)*sqrt(n)}}} Take the square root of {{{100}}} to get {{{10}}}.



{{{10*sqrt(2)*m*m*sqrt(n)}}} Take the square root of {{{m^2}}} to get {{{m}}}.



{{{10m^2*sqrt(2n)}}} Rearrange and multiply the terms.


==================================================


Answer:



So {{{sqrt(200*m^4*n)}}} simplifies to {{{10m^2*sqrt(2n)}}}



In other words, {{{sqrt(200*m^4*n)=10m^2*sqrt(2n)}}} where every variable is non-negative.