Question 200781
{{{(3*sqrt(2))*(-4*sqrt(10))}}} Start with the given expression.



{{{(3)(-4)*(sqrt(2)*sqrt(10))}}} Rearrange the terms.



{{{-12*(sqrt(2)*sqrt(10))}}} Multiply 3 and -4 to get -12



{{{-12*sqrt(2*10)}}} Combine the roots using the identity {{{sqrt(x)*sqrt(y)=sqrt(x*y)}}} 



{{{-12*sqrt(20)}}} Multiply 2 and 10 to get 20



{{{-12*sqrt(4*5)}}} Factor 20 to get 4*5. Note: one of the factors must be a perfect square.



{{{-12*sqrt(4)*sqrt(5)}}} Break up the roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}



{{{-12*2*sqrt(5)}}} Take the square root of 4 to get 2.



{{{-24*sqrt(5)}}} Multiply -12 and 2 to get -24



So {{{(3*sqrt(2))*(-4*sqrt(10))=-24*sqrt(5)}}}