Evaluate: $\sqrt{5} + 2 \sqrt{6} + \sqrt{8} - 2 \sqrt{15}$ .

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Solution

$\sqrt{5} + 2 \sqrt{6} + \sqrt{8} - 2 \sqrt{15} = \sqrt{5} + 2 \sqrt{2} \sqrt{3} + 2 \sqrt{2} - 2 \sqrt{3} \sqrt{5} = 2 \sqrt{2} (\sqrt{3} + 1) + \sqrt{5} (1 - 2 \sqrt{3}) = 2 \times 1.41 (1.73 + 1) + 2.23 (1 - 2 \times 1.73) = 7.69 - 5.48$
$= 2.21$ , which is the required value.

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