After rationalizing the numerator of (√3-√2)/(√3), the denominator in simplest form is:

1950 AMC 12 Problem 10

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10.

After rationalizing the numerator of

\dfrac{\sqrt3-\sqrt2}{\sqrt3},

the denominator in simplest form is:

\sqrt3(\sqrt3+\sqrt2)

\sqrt3(\sqrt3-\sqrt2)

3-\sqrt3\sqrt2

3+\sqrt6

None of these answers

Multiply the numerator and denominator by the conjugate of the numerator

The numerator becomes

(\sqrt3-\sqrt2)(\sqrt3+\sqrt2)=1

Multiplying by the conjugate of the numerator gives

\begin{aligned} &\frac{\sqrt3-\sqrt2}{\sqrt3} \cdot\frac{\sqrt3+\sqrt2}{\sqrt3+\sqrt2}\\ &=\frac{1}{\sqrt3(\sqrt3+\sqrt2)}\\ &=\frac{1}{3+\sqrt6}. \end{aligned}

Thus, the correct answer is D.