Question

Simplify: $(6\sqrt{2}-7\sqrt{3})(6\sqrt{2}-7\sqrt{3})$.

Answer 1

The given surds can be simplified as follows:

$(6\sqrt{2}-7\sqrt{3})(6\sqrt{2}-7\sqrt{3})=6\sqrt{2}(6\sqrt{2}-7\sqrt{3})-7\sqrt{3}(6\sqrt{2}-7\sqrt{3})$

$=(6\times 6\sqrt{2\times 2})-(6\times 7\sqrt{3\times 2})-(7\times 6\sqrt{3\times 2})+(7\times 7\sqrt{3\times 3})=(36\times 2)-42\sqrt{6}-42\sqrt{6}+(49\times 3)$

$=72-84\sqrt{6}+147=219-84\sqrt{6}$ .

Hence, $(6\sqrt{2}-7\sqrt{3})(6\sqrt{2}-7\sqrt{3})=219-84\sqrt{6}$ .