Question

Rationalize id="TexFormula1" title=" \frac{1}{2 \sqrt{7} + 3 \sqrt{3} } " alt=" \frac{1}{2 \sqrt{7} + 3 \sqrt{3} } " align="absmiddle" class="latex-formula">

Answer 1

$\dfrac{1}{2 \sqrt{7} + 3 \sqrt{3} }$

$= \dfrac{1}{2 \sqrt{7} + 3 \sqrt{3} } \times \dfrac{2 \sqrt{7} - 3 \sqrt{3}}{2 \sqrt{7} - 3 \sqrt{3}}$

$=\dfrac{2 \sqrt{7} - 3 \sqrt{3}}{(2\sqrt{7})^2 - (3\sqrt{3})^2}$

$=\dfrac{2 \sqrt{7} - 3 \sqrt{3}}{28 - 27}$

$=\dfrac{2 \sqrt{7} - 3 \sqrt{3}}{1}$

$=2 \sqrt{7} - 3 \sqrt{3}$