Question

Rút gọn
\(\left(\sqrt{5}+2\right).\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)
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Answer 1

\(\left(\sqrt{5}+2\right).\sqrt{17-4\sqrt{9+4\sqrt{5}}}=\left(\sqrt{5}+2\right).\sqrt{17-4\sqrt{\left(\sqrt{5}\right)^2+2.2.\sqrt{5}+2^2}}=\left(\sqrt{5}+2\right).\sqrt{17-4\sqrt{\left(\sqrt{5}+2\right)^2}}=\left(\sqrt{5}+2\right).\sqrt{17-4.\sqrt{5}-8}=\left(\sqrt{5}+2\right).\sqrt{9-4\sqrt{5}}=\left(\sqrt{5}+2\right).\sqrt{\left(\sqrt{5}\right)^2-2.2.\sqrt{5}+2^2}=\left(\sqrt{5}+2\right).\sqrt{\left(\sqrt{5}-2\right)^2}=\left(\sqrt{5}+2\right).\left(\sqrt{5}-2\right)=\left(\sqrt{5}\right)^2-4=5-4=1\)