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# rationalize the denominator

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Rationalize the denominator of $$\frac{\sqrt{32}}{\sqrt{16}-\sqrt{2}}$$. The answer can be written as $$\frac{A\sqrt{B}+C}{D}$$, where A, B, C, and D are integers, D is positive, and B is not divisible by the square of any prime. Find the minimum possible value of $$A+B+C+D$$.

Jul 19, 2020

$$\frac{\sqrt{32}}{\sqrt{16} - \sqrt{2}} = \frac{2 + 6 \sqrt{2}}{7}$$