Question 31715
{{{ (sqrt(8))/(2*(sqrt(5) + sqrt(6))) }}}
First thing you MUST do is rationalize the denominator by multiplying by the conjugate {{{ (sqrt(5)- sqrt(6)) }}}
{{{ ((sqrt(8))/(2*(sqrt(5) + sqrt(6))))((sqrt(5)- sqrt(6))/(sqrt(5)- sqrt(6))) }}}
{{{ ((sqrt(8))(sqrt(5)-sqrt(6)))/(2(sqrt(5)- sqrt(6))(sqrt(5)+ sqrt(6))) }}}
When multiplying by the conjugate, the roots cancel
{{{ ((sqrt(8))(sqrt(5)-sqrt(6)))/(2(5-6)) }}}
Multiply out the numerator
{{{ (sqrt(40) - sqrt(48))/(2(5-6)) }}}
Work out the roots
{{{ (2(sqrt(10)) - 2(sqrt(3)))/(2(5-6)) }}}
Reduce all parts by 2
{{{ (sqrt(10) - sqrt(3))/(5-6) }}}
work the denominator
{{{ (sqrt(10) - sqrt(3))/-1 }}}
Some instructors will allow you to leave it in this form ... otherwise change the signs of the numerator and drop the denominator
{{{ sqrt(3) - sqrt(10)) }}}