Question 193070
{{{sqrt(300x^4)/sqrt(5x)}}} Start with the given expression.



{{{sqrt((300x^4)/(5x))}}} Combine the roots.



{{{sqrt(60x^3)}}} Divide {{{(300x^4)/(5x)}}} to get {{{60x^3}}}



{{{sqrt(4*15*x^3)}}} Factor {{{60}}} into {{{4*15}}}



{{{sqrt(4*15*x^2*x)}}} Factor {{{x^3}}} into {{{x^2*x}}}



{{{sqrt(4)*sqrt(15)*sqrt(x^2)*sqrt(x)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{2*sqrt(15)*sqrt(x^2)*sqrt(x)}}} Take the square root of {{{4}}} to get {{{2}}}.



{{{2*sqrt(15)*x*sqrt(x)}}} Take the square root of {{{x^2}}} to get {{{x}}}.



{{{2x*sqrt(15x)}}} Rearrange and combine the terms.


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Answer:



So {{{sqrt(300x^4)/sqrt(5x)}}} simplifies to {{{2x*sqrt(15x)}}}



In other words, {{{sqrt(300x^4)/sqrt(5x)=2x*sqrt(15x)}}} where {{{x>0}}}