Question

Rationalise the denominator of 3-2 root3/2+ root 3​

Answer 1

$\underline{\bold{\sf{Rationalising\:denominator}}}\\\\\sf{Given,}\\\\\:\dfrac{3-2\sqrt{3}}{2+\sqrt{3}}\implies\:\bigg(\dfrac{3-2\sqrt{3}}{2+\sqrt{3}}\bigg)\bigg(\dfrac{2-\sqrt{3}}{2-\sqrt{3}}\bigg)\\\\\\\implies\:\dfrac{6+3\sqrt{3}-4\sqrt{3}-6}{4-3}\\\\\\\implies\:\dfrac{-\sqrt{3}}{1}=-\sqrt{3}$

Answer 2

$\tt\dfrac{3-2 \sqrt{3}}{2+ \sqrt{3}}$

$\implies \tt\dfrac{3-2\sqrt{3}}{2+ \sqrt{3}} \times \dfrac{2- \sqrt{3}}{2-\sqrt{3}}$

$\implies\tt\dfrac{6+ 3\sqrt{3}-4\sqrt{3}-6}{4-3}$

$\implies\tt\dfrac{-\sqrt{3}}{1} \implies -\sqrt{3}$