Question 243683

{{{sqrt(50*y^8)}}} Start with the given expression.



{{{sqrt(25*2*y^8)}}} Factor {{{50}}} into {{{25*2}}}



{{{sqrt(25*2*y^2*y^2*y^2*y^2)}}} Factor {{{y^8}}} into {{{y^2*y^2*y^2*y^2}}}



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



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



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



{{{5y^4*sqrt(2)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(50*y^8)}}} simplifies to {{{5y^4*sqrt(2)}}}



In other words, {{{sqrt(50*y^8)=5y^4*sqrt(2)}}} where {{{y>=0}}}