Question 186676
{{{5*sqrt(-6)*4*sqrt(-10)}}} Start with the given expression.



{{{5*sqrt(-1*6)*4*sqrt(-1*10)}}} Factor -6 into -1*6. Factor -10 into -1*10



{{{5*sqrt(-1)*sqrt(6)*4*sqrt(-1)*sqrt(10)}}} Break up the square root.



{{{5*i*sqrt(6)*4*i*sqrt(10)}}} Replace the square root of -1 with 'i' (note: {{{i=sqrt(-1)}}})



{{{(5*4)*(sqrt(6)*sqrt(10))*(i*i)}}} Rearrange the terms.



{{{(5*4)*(sqrt(6)*sqrt(10))*(i^2)}}} Multiply 'i' and 'i' to get {{{i^2}}}



{{{(5*4)*(sqrt(6)*sqrt(10))*(-1)}}} Replace {{{i^2}}} with -1. Remember, since  {{{i=sqrt(-1)}}}, then {{{i^2=-1}}}



{{{(5*4*(-1))*(sqrt(6)*sqrt(10))}}} Rearrange the terms again



{{{-20*(sqrt(6)*sqrt(10))}}} Multiply



{{{-20*sqrt(6*10)}}} Combine the roots.



{{{-20*sqrt(60))}}} Multiply



{{{-20*sqrt(4*15)}}} Factor 60 into 4*15. Note: one factor is a perfect square



{{{-20*sqrt(4)*sqrt(15)}}} Break up the square root.



{{{-20*2*sqrt(15)}}} Take the square root of 4 to get 2



{{{-40*sqrt(15)}}} Multiply



So {{{5*sqrt(-6)*4*sqrt(-10)=-40*sqrt(15)}}}