Question 179471


{{{3*sqrt(180*h^4)}}} Start with the given expression.



{{{3*sqrt(36*5*h^4)}}} Factor {{{180}}} into {{{36*5}}}



{{{3*sqrt(36*5*h^2*h^2)}}} Factor {{{h^4}}} into {{{h^2*h^2}}}



{{{3*sqrt(36)*sqrt(5)*sqrt(h^2)*sqrt(h^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{3*6*sqrt(5)*sqrt(h^2)*sqrt(h^2)}}} Take the square root of {{{36}}} to get {{{6}}}.



{{{3*6*sqrt(5)*h*h}}} Take the square root of {{{h^2}}} to get {{{h}}}.



{{{18h^2*sqrt(5)}}} Rearrange and multiply the terms.


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Answer:



So {{{3*sqrt(180*h^4)}}} simplifies to {{{18h^2*sqrt(5)}}}



In other words, {{{3*sqrt(180*h^4)=18h^2*sqrt(5)}}} where every variable is positive.