Question 109224
#1

{{{sqrt(200*y^6)}}}Start with the given expression

{{{sqrt(100*2*y^6)}}} Factor {{{200}}} into {{{100*2}}}
 
{{{sqrt(100*2*y^2*y^2*y^2)}}} Factor {{{y^6}}} into {{{y^2*y^2*y^2}}}
 
{{{sqrt(100)*sqrt(2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)}}} Break up the square root using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
{{{10*sqrt(2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)}}} Take the square root of the perfect square {{{100}}} to get 10 
 
{{{10*sqrt(2)*y*y*y}}} Take the square root of the perfect squares {{{y^2}}} to get {{{y}}} 
 
{{{10*sqrt(2)*y^3}}} Multiply the common terms 

{{{10*y^3*sqrt(2)}}} Rearrange the terms 



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First let's simplify the numerator


{{{sqrt(5*m^2)}}}Start with the numerator

 
{{{sqrt(5)*sqrt(m^2)}}} Break up the square root using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 
{{{sqrt(5)*m}}} Take the square root of the perfect square {{{m^2}}} to get {{{m}}} 
 

{{{m*sqrt(5)}}} Rearrange the terms 



So the expression {{{sqrt(5m^2)/2}}} simplifies to 



{{{m*sqrt(5)/2}}}