33 − 3\frac{3}{3\; -\; \sqrt{3}}3−33
Rationalize
=33 − 6×3 + 63 + 6= \frac{3}{3\; -\; \sqrt{6}} \times \frac{3\; +\; \sqrt{6}}{3\; +\; \sqrt{6}}=3−63×3+63+6
=3(3 + 6)(3 − 6)(3 + 6)= \frac{3(3\; +\; \sqrt{6})}{(3\; -\; \sqrt{6})(3\; +\; \sqrt{6})}=(3−6)(3+6)3(3+6)
=3(3 + 6)9 − 6=3(3 + 6)3= \frac{3(3\; +\; \sqrt{6})}{9\; -\; 6} = \frac{3(3\; +\; \sqrt{6})}{3}=9−63(3+6)=33(3+6)
∴ 3 + √6
