Question 225353
Rationalizing denominators means to eliminate any irrational numbers (like square roots) from the denominator <i>using proper Algebra</i>! Your expression has a binomial (two term) denominator. To rationalize binomial denominators we use the following pattern: {{{(a+b)(a-b) = a^2 - b^2}}}. This pattern shows how to take a two term expression, like (a+b) or (a-b), and make it turn into an expression of perfect squares, {{{a^2 - b^2}}}. Pairs of expressions like (a+b) and (a-b) are called conjugates. And when you multiply conjugates you get an expression containing nothing but perfect squares.<br>
Let's use this on your problem:
{{{2/(sqrt(3) + sqrt(2))}}}
Your denominator is of the form (a-b). So we will multiply the numerator and denominator by its conjugate, (a+b):
{{{(2/(sqrt(3) + sqrt(2)))*((sqrt(3)-sqrt(2))/(sqrt(3)-sqrt(2)))}}}
Using the distributive property on top and the pattern (or FOIL) on the bottom:
{{{(2sqrt(3) + 2sqrt(2))/((sqrt(3))^2 - (sqrt(2))^2)}}}
Simplifying:
{{{(2sqrt(3) + 2sqrt(2))/(3 - 2)}}}
{{{(2sqrt(3) + 2sqrt(2))/1}}}
{{{2sqrt(3) + 2sqrt(2)}}}