Rationalize the denominator of $\displaystyle \frac{1}{\sqrt{5} - \sqrt{2}}$. With your answer in the form $\displaystyle \frac{\sqrt{A} + \sqrt{B}}{C}$, and the fraction in lowest terms, what is $A + B + C$?
+23252 To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator.
The conjugate of sqrt(5) - sqrt(2) is sqrt(5) + sqrt(2).
1/ [ sqrt(5) - sqrt(2) ] · [ sqrt(5) + sqrt(2) ] / [ sqrt(5) + sqrt(2) ]
= [ sqrt(5) + sqrt(2) ] / { [ sqrt(5) - sqrt(2) ] · [ sqrt(5) + sqrt(2) ] }
= [ sqrt(5) + sqrt(2) ] / [ 5 - 2 ]
= [ sqrt(5) + sqrt(2) ] / 3
A is 5, B is 2 and C is 3 ...
