$$(\sqrt{6}-\sqrt{11})(2\sqrt{6}-3\sqrt{11})$$
$45-5\sqrt{66}\approx 4.379807977$
$$2\left(\sqrt{6}\right)^{2}-3\sqrt{6}\sqrt{11}-2\sqrt{11}\sqrt{6}+3\left(\sqrt{11}\right)^{2}$$
$$2\times 6-3\sqrt{6}\sqrt{11}-2\sqrt{11}\sqrt{6}+3\left(\sqrt{11}\right)^{2}$$
$$12-3\sqrt{6}\sqrt{11}-2\sqrt{11}\sqrt{6}+3\left(\sqrt{11}\right)^{2}$$
$$12-3\sqrt{66}-2\sqrt{11}\sqrt{6}+3\left(\sqrt{11}\right)^{2}$$
$$12-3\sqrt{66}-2\sqrt{66}+3\left(\sqrt{11}\right)^{2}$$
$$12-5\sqrt{66}+3\left(\sqrt{11}\right)^{2}$$
$$12-5\sqrt{66}+3\times 11$$
$$12-5\sqrt{66}+33$$
$$45-5\sqrt{66}$$
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