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Rationalisation

Simplify 3+...

Question

Simplify $(3 + \sqrt{2}) (6 + 4 \sqrt{3})$

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Solution

$(3 + \sqrt{2}) (6 + 4 \sqrt{3}) = 2 (3 + \sqrt{2}) (3 + 2 \sqrt{3}) = 2 (9 + 3 \sqrt{2} + 6 \sqrt{3} + 4 \sqrt{3}) = 18 + 20 \sqrt{3} + 6 \sqrt{2}$

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