Question

Rationalise the denominators (viii)
2√3 - 3√ 2 ___by_____ 3√2 + 2√3​

Answer 1

$= \frac{2 \sqrt{3} - 3 \sqrt{2} }{2\sqrt{3} + 3 \sqrt{2} } \\ = \frac{2 \sqrt{3} - 3 \sqrt{2} }{2 \sqrt{3} + 3 \sqrt{2} } \times \frac{2 \sqrt{3} - 3 \sqrt{2} }{2 \sqrt{3} - 3 \sqrt{2} } \\ = \frac{ ({2 \sqrt{3} - 3 \sqrt{2} })^{2} }{( {2 \sqrt{3} })^{2} - ( {3 \sqrt{2} })^{2} } \\ = \frac{12 + 18 - 12 \sqrt{6} }{12 - 18} \\ = \frac{30 - 12 \sqrt{6} }{ - 6} \\ = - 5 + 2 \sqrt{6}$