Simplify 2√2−√3√2+√3

Question 1 Report

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

\sqrt{6} - 7

\sqrt{6} - 7

\sqrt{6} - 1

\sqrt{6} + 1

Answer Details

$= \frac{2 \sqrt{2} - \sqrt{3}}{\sqrt{2} + \sqrt{3}} \times \frac{\sqrt{2} - \sqrt{3}}{\sqrt{2} + \sqrt{3}}$
$= \frac{2 \sqrt{2} (\sqrt{2}) + (2 \sqrt{2}) (- \sqrt{3}) - \sqrt{3} (\sqrt{2}) - \sqrt{3} (- \sqrt{3})}{(\sqrt{2})^{2} - (\sqrt{3})^{2}}$
$= \frac{2 \times 2 - 2 \sqrt{6} - \sqrt{6} + 3}{2 - 3}$
$= \frac{4 - 3 \sqrt{6} + 3}{- 1}$
$= \frac{7 - 3 \sqrt{6}}{- 1}$
$= \frac{7}{- 1} - \frac{3 \sqrt{6}}{- 1}$
$= - 7 + 3 \sqrt{6}$
$= 3 \sqrt{6} - 7$

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