Question

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Answer 1

\(Q=\dfrac{\sqrt{2}+\sqrt{5-\sqrt{24}}}{\sqrt{12}}=\dfrac{\sqrt{2}+\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}}{2\sqrt{3}}=\dfrac{\sqrt{2}+\left|\sqrt{3}-\sqrt{2}\right|}{2\sqrt{3}}\)

\(=\dfrac{\sqrt{2}+\sqrt{3}-\sqrt{2}}{2\sqrt{3}}=\dfrac{\sqrt{3}}{2\sqrt{3}}=\dfrac{1}{2}\)