How do you divide 4+√23√3−√6?

1 Answer
Alan P.
Mar 24, 2015

Simplify the denominator by remembering that
(a−b)×(a+b)=(a2−b2)
and therefore we can get rid of the roots in the denominator by multiplying by 3√3+√6

Of course if we multiply the denominator by 3√3+√6 we will have to multiply the numerator by that amount as well.

4+√23√3−√6⋅3√3+√63√3+√6

=4(3√3+√6)+√2(3√3+√6)27−6

=12√3+4√6+3√6+√1221

=12√3+7√6+√1221

or
√312+7√2+√421

=√314+7√221

=7√3⋅2+√23

or, possibly
=72+√2√3

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