Question 86160
{{{sqrt(12x^3/5)}}} Start with the given expression


{{{sqrt(12x^3)/sqrt(5)}}} Break up the square roots using the identity {{{sqrt(x/y)=sqrt(x)/sqrt(y)}}}

Now lets simplify the numerator {{{sqrt(12x^3)}}}

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{{{sqrt(12*x^3)}}} Start with the given expression

{{{sqrt(4*3*x^3)}}} Factor {{{12}}} into {{{4*3}}}
 
{{{sqrt(4*3*x*x^2)}}} Factor {{{x^3}}} into {{{x*x^2}}}
 
{{{sqrt(4)*sqrt(3)*sqrt(x)*sqrt(x^2)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
{{{2*sqrt(3)*sqrt(x)*sqrt(x^2)}}} Take the square root of the perfect square {{{4}}} to get 2 
 
{{{2*sqrt(3)*sqrt(x)*x}}} Take the square root of the perfect squares and {{{x^2}}} to get and {{{x}}} 
 
{{{2*sqrt(3)*x*sqrt(x)}}} Multiply the common terms 

{{{2*x*sqrt(x)*sqrt(3)}}} Rearrange the terms 

{{{2*x*sqrt(3x)}}} Group the square root terms 

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So the expression


{{{sqrt(12x^3/5)}}}


simplifies to 


{{{(2*x*sqrt(3x))/sqrt(5)}}}