Rationalize √2+√3√2−√3

Question 1 Report

Rationalize $\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}$

- 5 - 2 \sqrt{6}

- 5 + 3 \sqrt{2}

5 - 2 \sqrt{3}

5 + 2 \sqrt{6}

Answer Details

$\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}$
= $(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}) (\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} + \sqrt{3}})$
= $\frac{2 + \sqrt{6} + \sqrt{6} + 3}{2 - \sqrt{6} + \sqrt{6} - 3}$
= $\frac{5 + 2 \sqrt{6}}{- 1}$
= $- 5 - 2 \sqrt{6}$

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