$$(5\sqrt{3}-2\sqrt{2})\times(3\sqrt{2}+\sqrt{3})$$
$13\sqrt{6}+3\approx 34.843366656$
$$15\sqrt{3}\sqrt{2}+5\left(\sqrt{3}\right)^{2}-6\left(\sqrt{2}\right)^{2}-2\sqrt{2}\sqrt{3}$$
$$15\sqrt{6}+5\left(\sqrt{3}\right)^{2}-6\left(\sqrt{2}\right)^{2}-2\sqrt{2}\sqrt{3}$$
$$15\sqrt{6}+5\times 3-6\left(\sqrt{2}\right)^{2}-2\sqrt{2}\sqrt{3}$$
$$15\sqrt{6}+15-6\left(\sqrt{2}\right)^{2}-2\sqrt{2}\sqrt{3}$$
$$15\sqrt{6}+15-6\times 2-2\sqrt{2}\sqrt{3}$$
$$15\sqrt{6}+15-12-2\sqrt{2}\sqrt{3}$$
$$15\sqrt{6}+3-2\sqrt{2}\sqrt{3}$$
$$15\sqrt{6}+3-2\sqrt{6}$$
$$13\sqrt{6}+3$$
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$13 \sqrt{6} + 3 = 34.843366656$
