Question

rationalizes 7 root of three - 5 root of 2 divided by root of 48 + root of 18​

Answer 1

Answer:

$\frac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18} } \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{4 \sqrt{3} - 3 \sqrt{2} } \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{4 \sqrt{3} - 3 \sqrt{2} } \times \frac{4 \sqrt{3} + 3\sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \\ = \frac{(7 \sqrt{3} - 5 \sqrt{2} )(4 \sqrt{3} + 3 \sqrt{2} )}{ {(4 \sqrt{3}) }^{2} - ( {3 \sqrt{2} )}^{2}} \\ \frac{28 \times 3 + 21 \sqrt{6} - 20 \sqrt{6} - 30}{16 \times 3 - 9 \times 2} \\ \frac{54 + \sqrt{6} }{30}$

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