Rationalize the denominator and then simplify.

Name: Rationalize the denominator and then simplify.
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Question

Quizplus · Accepted Answer

To rationalize the denominator, we need to multiply the numerator and the denominator by the conjugate of the denominator, which is $\sqrt{2}-\sqrt{3}$:
$$\frac{1}{\sqrt{2}+\sqrt{3}}=\frac{1}{\sqrt{2}+\sqrt{3}}\cdot\frac{\sqrt{2}-\sqrt{3}}{\sqrt{2}-\sqrt{3}}=\frac{\sqrt{2}-\sqrt{3}}{-1}=\sqrt{3}-\sqrt{2}$$
The only choice that matches this result is D.

Rationalize the Denominator and Then Simplify