Question 282541

{{{sqrt(48*p^3)}}} Start with the given expression.



{{{sqrt(16*3*p^3)}}} Factor {{{48}}} into {{{16*3}}}



{{{sqrt(16*3*p^2*p)}}} Factor {{{p^3}}} into {{{p^2*p}}}



{{{sqrt(16)*sqrt(3)*sqrt(p^2)*sqrt(p)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{4*sqrt(3)*sqrt(p^2)*sqrt(p)}}} Take the square root of {{{16}}} to get {{{4}}}.



{{{4*sqrt(3)*p*sqrt(p)}}} Take the square root of {{{p^2}}} to get {{{p}}}.



{{{4p*sqrt(3p)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(48*p^3)}}} simplifies to {{{4p*sqrt(3p)}}}



In other words, {{{sqrt(48*p^3)=4p*sqrt(3p)}}} where {{{p>=0}}}