Question

2root 5+3root2 upon2root 5-3root2​

Answer 1

$\frac{2 \sqrt{5} + 3 \sqrt{2} }{ 2 \sqrt{5 } - 3 \sqrt{2} } \\ \\ by \: rationalising \\ \\ \frac{2 \sqrt{5} + 3 \sqrt{2} }{ 2 \sqrt{5 } - 3 \sqrt{2} } \times \frac{2 \sqrt{5} + 3 \sqrt{2} }{ 2 \sqrt{5 } + 3 \sqrt{2} } \\ \\ = \frac{ {(2 \sqrt{5} } + 3 \sqrt{2}) ^{2} }{(2 \sqrt{5} )^{2} - (3 \sqrt{2})^{2} } \\ \\ = \frac{(2 \sqrt{5} )^{2} + (3 \sqrt{2} )^{2} + 2(2 \sqrt{5} )(3 \sqrt{2}) }{(4 \times 5) - (9 \times 2)} \\ \\ = \frac{(4 \times 5) + ( 9\times 2) + 12 \sqrt{10} }{20 - 18} \\ \\ = \frac{20 + 18 + 12 \sqrt{10} }{2} \\ \\ = \frac{38 + 12 \sqrt{10} }{2} \\ \\ = \frac{2(19 + 6 \sqrt{10}) }{2} \\ \\ = 19 + 6 \sqrt{10}$

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