Question 86383
<pre>
{{{2/(sqrt(3) + sqrt(2))}}}
Can you help me rationalize the denominator? I really apprecuate your help. It
would help so much if you could show me how you do this.

Form the conjugate surd of the denominator:
1. Copy the first term
2. Copy the second term with the sign changed.

The conjugate surd of the denominator {{{sqrt(3)+sqrt(2)}}} is
{{{sqrt(3) - sqrt(2)}}}.  Write it over itself to form a 
fraction equal to 1:

{{{(sqrt(3) - sqrt(2))/(sqrt(3) - sqrt(2))}}}

Multiply the original eqpression by that fraction.  It doesn't
change the value because the fraction equals 1.

    
{{{2/(sqrt(3) + sqrt(2))}}}×{{{(sqrt(3) - sqrt(2))/(sqrt(3) - sqrt(2))}}}

{{{ 2 (sqrt(3) - sqrt(2) )/((sqrt(3) - sqrt(2))(sqrt(3)+sqrt(2)))  }}}

FOIL out the denominator:

{{{ 2 (sqrt(3) - sqrt(2) )/(3 + sqrt(6)-sqrt(6)-2)  }}}

Cancel the terms in {{{sqrt(6)}}} in the bottom

{{{ 2 (sqrt(3) - sqrt(2) )/(3-2)  }}}

{{{ 2 (sqrt(3) - sqrt(2) )/1  }}}

{{{ 2 (sqrt(3) - sqrt(2) )  }}}

You can multiply that out if you like and get

{{{2sqrt(3) - 2sqrt(2)}}}

Edwin</pre>