$$(\sqrt{5}+\sqrt{8})(\sqrt{9}+\sqrt{6})$$
$\sqrt{30}+3\sqrt{5}+4\sqrt{3}+6\sqrt{2}\approx 27.598914112$
$$\left(\sqrt{5}+2\sqrt{2}\right)\left(\sqrt{9}+\sqrt{6}\right)$$
$$\left(\sqrt{5}+2\sqrt{2}\right)\left(3+\sqrt{6}\right)$$
$$3\sqrt{5}+\sqrt{5}\sqrt{6}+6\sqrt{2}+2\sqrt{2}\sqrt{6}$$
$$3\sqrt{5}+\sqrt{30}+6\sqrt{2}+2\sqrt{2}\sqrt{6}$$
$$3\sqrt{5}+\sqrt{30}+6\sqrt{2}+2\sqrt{2}\sqrt{2}\sqrt{3}$$
$$3\sqrt{5}+\sqrt{30}+6\sqrt{2}+2\times 2\sqrt{3}$$
$$3\sqrt{5}+\sqrt{30}+6\sqrt{2}+4\sqrt{3}$$
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