Question

\(\dfrac{\sqrt{\sqrt{15}-\sqrt{6}}+\sqrt{\sqrt{15}+\sqrt{6}}}{\sqrt{\sqrt{15}+3}}\)

Answer 1

\(\dfrac{\sqrt{\sqrt{15}-\sqrt{6}}+\sqrt{\sqrt{15}+\sqrt{6}}}{\sqrt{\sqrt{15}+3}}\)

\(=\dfrac{\sqrt{\sqrt{3}.\left(\sqrt{5}-\sqrt{3}\right)}+\sqrt{\sqrt{3}.\left(\sqrt{5}+\sqrt{3}\right)}}{\sqrt{\sqrt{3}.\left(\sqrt{5}+\sqrt{3}\right)}}\)

\(=\dfrac{\sqrt{\sqrt{3}}.\left[\left(\sqrt{5}-\sqrt{3}\right)+\left(\sqrt{5}+\sqrt{3}\right)\right]}{\sqrt{\sqrt{3}.\left(\sqrt{5}+\sqrt{3}\right)}}\)

\(=\dfrac{\sqrt{5}-\sqrt{3}+\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}=\dfrac{2\sqrt{5}}{\sqrt{5}+\sqrt{3}}\)

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