Question 303462


{{{sqrt(75*y^4*w^3)}}} Start with the given expression.



{{{sqrt(25*3*y^4*w^3)}}} Factor {{{75}}} into {{{25*3}}}



{{{sqrt(25*3*y^2*y^2*w^3)}}} Factor {{{y^4}}} into {{{y^2*y^2}}}



{{{sqrt(25*3*y^2*y^2*w^2*w)}}} Factor {{{w^3}}} into {{{w^2*w}}}



{{{sqrt(25)*sqrt(3)*sqrt(y^2)*sqrt(y^2)*sqrt(w^2)*sqrt(w)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{5*sqrt(3)*sqrt(y^2)*sqrt(y^2)*sqrt(w^2)*sqrt(w)}}} Take the square root of {{{25}}} to get {{{5}}}.



{{{5*sqrt(3)*sqrt(y^2)*sqrt(y^2)*w*sqrt(w)}}} Take the square root of {{{w^2}}} to get {{{w}}}.



{{{5*sqrt(3)*y*y*w*sqrt(w)}}} Take the square root of {{{y^2}}} to get {{{y}}}.



{{{5wy^2*sqrt(3w)}}} Rearrange and multiply the terms.


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


Answer:



So {{{sqrt(75*y^4*w^3)}}} simplifies to {{{5wy^2*sqrt(3w)}}}



In other words, {{{sqrt(75*y^4*w^3)=5wy^2*sqrt(3w)}}} where every variable is non-negative.