Question 191973
{{{sqrt(10x)*sqrt(8x)}}} Start with the given expression.



{{{sqrt(10x*8x)}}} Combine the roots



{{{sqrt(80x^2)}}} Multiply



{{{sqrt(16*5*x^2)}}} Factor {{{80}}} into {{{16*5}}}



{{{sqrt(16)*sqrt(5)*sqrt(x^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{4*sqrt(5)*sqrt(x^2)}}} Take the square root of {{{16}}} to get {{{4}}}.



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



{{{4x*sqrt(5)}}} Rearrange the terms.


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Answer:



So {{{sqrt(10x)*sqrt(8x)}}} simplifies to {{{4x*sqrt(5)}}}



In other words, {{{sqrt(10x)*sqrt(8x)=4x*sqrt(5)}}} where {{{x>=0}}}