Rút gọn biểu thức: `a,sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}` `b,\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}`

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1. Đáp án:

    

   Giải thích các bước giải:

    

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2. a) $\sqrt[]{5}-\sqrt[]{3-\sqrt[]{29-12\sqrt[]{5}}}$

   $=\sqrt[]{5}-\sqrt[]{3-\sqrt[]{(2\sqrt[]{5})^2-2.2\sqrt[]{5}.3+3^2}}$

   $=\sqrt[]{5}-\sqrt[]{3-\sqrt[]{(2\sqrt[]{5}-3)^2}}$

   $=\sqrt[]{5}-\sqrt[]{3-(2\sqrt[]{5}-3)}$

   $=\sqrt[]{5}-\sqrt[]{6-2\sqrt[]{5}}$

   $=\sqrt[]{5}-\sqrt[]{(\sqrt[]{5})^2-2\sqrt[]{5}.1+1}$

   $=\sqrt[]{5}-\sqrt[]{(\sqrt[]{5}-1)^2}$

   $=\sqrt[]{5}-(\sqrt[]{5}-1)$

   $=1$

   b) $\sqrt[]{4+\sqrt[]{8}}.\sqrt[]{2+\sqrt[]{2+\sqrt[]{2}}}.\sqrt[]{2-\sqrt[]{2+\sqrt[]{2}}}$

   $=\sqrt[]{4+\sqrt[]{8}}.\sqrt[]{(2+\sqrt[]{2+\sqrt[]{2}})(2-\sqrt[]{2+\sqrt[]{2}})}$

   $=\sqrt[]{4+\sqrt[]{8}}.\sqrt[]{4-(2+\sqrt[]{2})}$

   $=\sqrt[]{4+\sqrt[]{8}}.\sqrt[]{2-\sqrt[]{2}}$

   $=\sqrt[]{(4+\sqrt[]{8})(2-\sqrt[]{2})}$

   $=\sqrt[]{8-4\sqrt[]{2}+2\sqrt[]{8}-4}$

   $=\sqrt[]{8-4-4\sqrt[]{2}+2.2\sqrt[]{2}}$

   $=\sqrt[]{4}$

   $=2$

    

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