Question 874139
To rationalize the denominator, we multiply top and bottom of the given fraction by {{{sqrt(2)}}}. Doing so gives us...



{{{8/(7*sqrt(2))}}}



{{{(8*sqrt(2))/(7*sqrt(2)*sqrt(2))}}}



{{{(8*sqrt(2))/(7*sqrt(2*2))}}}



{{{(8*sqrt(2))/(7*sqrt(4))}}}



{{{(8*sqrt(2))/(7*sqrt(2^2))}}}



{{{(8*sqrt(2))/(7*2)}}}



{{{(4*2*sqrt(2))/(7*2)}}}



{{{(4*highlight(2)*sqrt(2))/(7*highlight(2))}}}



{{{(4*cross(2)*sqrt(2))/(7*cross(2))}}}



{{{(4*sqrt(2))/(7)}}}



=======================================================



So, {{{8/(7*sqrt(2))=(4*sqrt(2))/(7)}}}