Question

Rationalise 3√5+7√2/√45-√48

Answer 1

Answer:

$\frac{3 \sqrt{5} + 7 \sqrt{2} }{ \sqrt{45} - \sqrt{48} } \\ = \frac{3 \sqrt{5} + 7 \sqrt{2} }{ \sqrt{3 \times 3 \times 5} - \sqrt{4 \times 4 \times 3} } \\ = \frac{3 \sqrt{5} + 7 \sqrt{2} }{3 \sqrt{5} - 4 \sqrt{3} } \\ = \frac{3 \sqrt{5} + 7 \sqrt{2} }{3 \sqrt{5} - 4 \sqrt{3} } \times \frac{3 \sqrt{5} + 4 \sqrt{3} }{3 \sqrt{5} + 4 \sqrt{3} } \\ = \frac{(3 \sqrt{5} + 7 \sqrt{2} )(3 \sqrt{5} + 4 \sqrt{3} )}{( {3 \sqrt{5}) }^{2} - ({4 \sqrt{3}) }^{2} } \\ = \frac{9 \times 5 + 21 \sqrt{10} + 12 \sqrt{15} + 28 \sqrt{6} }{9 \times 5 - 4 \times 3} \\ = \frac{45 + 21 \sqrt{10} + 12 \sqrt{15} + 28 \sqrt{6} }{45 - 12} \\ = \frac{45 + 21 \sqrt{10} + 12 \sqrt{15} + 28 \sqrt{6} }{33}$