Question 33984
{{{ root (3, 3) / (sqrt(7) + sqrt(10)) }}}
To rationalize the denominator you must multipy by the conjugate.
or in other words ...
{{{ (sqrt(7) - sqrt(10)) }}}
By doing this, when you foil, the middle term will cancel out.
Remember ...
{{{ (x+y)(x-y) = x^2 - y^2 }}}
so ... we will multiply the numerator and denominator by the conjugate.
{{{ (root (3, 3))(sqrt(7) - sqrt(10)) / (sqrt(7) + sqrt(10))(sqrt(7) - sqrt(10)) }}}
The denominator then follows the rule and we end up with ...
{{{ (root (3, 3))(sqrt(7) - sqrt(10)) / (7-10) }}}
{{{ (root (3, 3))(sqrt(7) - sqrt(10)) / -3 }}}
since the top numbers are cube roots and squareroots ... they can not be combined in radical form.