Question

rationalise
$4 \sqrt{3} \div 2 - \sqrt{2}$
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Answer 1

Step-by-step explanation:

$4 \sqrt{3} \div 2 - \sqrt{2} \\ \frac{4 \sqrt{3} }{2 - \sqrt{2} } = \frac{4 \sqrt{3} }{2 - \sqrt{2} } \times \frac{2 + \sqrt{2} }{2 + \sqrt{2} } \\ \frac{4 \sqrt{3}(2 + \sqrt{2} ) }{ {2}^{2} - ({ \sqrt{2} })^{2} } = \frac{8 \sqrt{3} + 4 \sqrt{6} }{4 - 2} \\ \frac{8 \sqrt{3} + 4 \sqrt{6} }{2} = 4 \sqrt{3} + 2 \sqrt{6}$