Question 88353
{{{sqrt(2t^5)sqrt(10t^4)}}}


{{{sqrt(2t^5*10t^4)}}} Combine the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}


{{{sqrt(20t^9)}}} Multiply




{{{sqrt(4*5*t^9)}}} Factor {{{20}}} into {{{4*5}}}
 
{{{sqrt(4*5*t*t^2*t^2*t^2*t^2)}}} Factor {{{t^9}}} into {{{t*t^2*t^2*t^2*t^2}}}
 
{{{sqrt(4)*sqrt(5)*sqrt(t)*sqrt(t^2)*sqrt(t^2)*sqrt(t^2)*sqrt(t^2)}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
{{{2*sqrt(5)*sqrt(t)*sqrt(t^2)*sqrt(t^2)*sqrt(t^2)*sqrt(t^2)}}} Take the square root of the perfect square {{{4}}} to get 2 
 
{{{2*sqrt(5)*sqrt(t)*t*t*t*t}}} Take the square root of each of the perfect squares {{{t^2}}} to get {{{t}}} 
 
{{{2*sqrt(5)*t^4*sqrt(t)}}} Multiply the common terms 

{{{2*t^4*sqrt(t)*sqrt(5)}}} Rearrange the terms 

{{{2*t^4*sqrt(5t)}}} Group the square root terms 





Check:

{{{sqrt(2(3)^5)sqrt(10(3)^4)}}} Plug in {{{x=3}}} (any value will do)


{{{sqrt(2*243)sqrt(10*81)}}}


{{{(22.04540)(28.46049)}}}


{{{627.423}}}



Now lets check our answer

{{{2*(3)^4*sqrt(5(3))}}}  Plug in {{{x=3}}}


{{{2*(3)^4*sqrt(15)}}} 


{{{2*81*sqrt(15)}}} 


{{{162*sqrt(15)}}}


{{{162*3.872983}}} 


{{{627.423}}}


works