\(\sqrt{2-\sqrt{3}}\left(\sqrt{5}+\sqrt{2}\right)=\dfrac{\sqrt{3-2\sqrt{3}+1}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{2}}=\dfrac{\sqrt{\left(\sqrt{3}-1\right)^2}\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{2}}=\dfrac{|\sqrt{3}-1|\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{2}}=\dfrac{\left(\sqrt{3}-1\right)\left(\sqrt{5}+\sqrt{2}\right)}{\sqrt{2}}\)
Giải:
\(\sqrt{2-\sqrt{3}}\left(\sqrt{5}+\sqrt{2}\right)\)
\(=\sqrt{5}\sqrt{2-\sqrt{3}}+\sqrt{2}\sqrt{2-\sqrt{3}}\)
\(=\sqrt{5\left(2-\sqrt{3}\right)}+\sqrt{2\left(2-\sqrt{3}\right)}\)
\(=\sqrt{10-5\sqrt{3}}+\sqrt{4-2\sqrt{3}}\)
\(=\sqrt{10-5\sqrt{3}}+\sqrt{3-2\sqrt{3}+1}\)
\(=\sqrt{10-5\sqrt{3}}+\sqrt{\left(\sqrt{3}-1\right)^2}\)
\(=\sqrt{10-5\sqrt{3}}+\sqrt{3}-1\)
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