Question 142360
{{{sqrt(3)/sqrt(8)}}} Start with the given expression



{{{(sqrt(3)/sqrt(8))(sqrt(8)/sqrt(8))}}} Multiply both the numerator and denominator by {{{sqrt(8)}}}



{{{(sqrt(3)sqrt(8))/(sqrt(8)sqrt(8))}}} Combine the fractions




{{{sqrt(3*8)/sqrt(8*8)}}} Combine the square roots. Remember {{{sqrt(x)*sqrt(y)=sqrt(x*y)}}}



{{{sqrt(24)/sqrt(64)}}} Multiply




{{{sqrt(24)/8}}} Take the square root of 64 to get 8




{{{sqrt(4*6)/8}}} Factor 24 into 4*6
 


{{{(sqrt(4)*sqrt(6))/8}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}
 


{{{(2*sqrt(6))/8}}} Take the square root of the perfect square 4 to get 2 



{{{(1*sqrt(6))/4}}} Reduce {{{2/8}}} to get {{{1/4}}}



{{{sqrt(6)/4}}} Simplify
 



So the expression {{{sqrt(3)/sqrt(8)}}} simplifies to {{{sqrt(6)/4}}}