Câu hỏi của chi mai Nguyen

Question

$\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}}$$B=\frac{\sqrt{15}-\sqrt{6}}{\sqrt{35}-\sqrt{14}}$$C=\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{4+2\sqrt{3}}}}$Rút gọn Giải giúp mình với mình cần gấp

Edogawa Conan · Accepted Answer

$A=\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}}=\sqrt{\left(\sqrt{2}+1\right)^2}+\sqrt{\left(\sqrt{2}-1\right)^2}$$=\sqrt{2}+1+\sqrt{2}-1=2\sqrt{2}$$B=\frac{\sqrt{15}-\sqrt{6}}{\sqrt{35}-\sqrt{14}}=\frac{\sqrt{3}.\sqrt{5}-\sqrt{2}.\sqrt{3}}{\sqrt{5}.\sqrt{7}-\sqrt{2}.\sqrt{7}}=\frac{\sqrt{3}\left(\sqrt{5}-\sqrt{2}\right)}{\sqrt{7}\left(\sqrt{5}-\sqrt{2}\right)}=\frac{\sqrt{3}}{\sqrt{7}}=\sqrt{\frac{3}{7}}$$C=\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{4+2\sqrt{3}}}}$$C=\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{\left(\sqrt{3}+1\right)^2}}}$$C=\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{3}-1}}$$C=\sqrt{6+2\sqrt{2}.\sqrt{2-\sqrt{3}}}$$C=\sqrt{6+2\sqrt{4-2\sqrt{3}}}$$C=\sqrt{6+2\sqrt{\left(\sqrt{3}-1\right)^2}}$$C=\sqrt{6+2.\left(\sqrt{3}-1\right)}$$C=\sqrt{6+2\sqrt{3}-2}$$C=\sqrt{4+2\sqrt{3}}$$C=\sqrt{\left(\sqrt{3}+1\right)^2}=\sqrt{3}+1$Câu trả lời: $A=\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}}=\sqrt{\left(\sqrt{2}+1\right)^2}+\sqrt{\left(\sqrt{2}-1\right)^2}$$=\sqrt{2}+1+\sqrt{2}-1=2\sqrt{2}$$B=\frac{\sqrt{15}-\sqrt{6}}{\sqrt{35}-\sqrt{14}}=\frac{\sqrt{3}.\sqrt{5}-\sqrt{2}.\sqrt{3}}{\sqrt{5}.\sqrt{7}-\sqrt{2}.\sqrt{7}}=\frac{\sqrt{3}\left(\sqrt{5}-\sqrt{2}\right)}{\sqrt{7}\left(\sqrt{5}-\sqrt{2}\right)}=\frac{\sqrt{3}}{\sqrt{7}}=\sqrt{\frac{3}{7}}$$C=\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{4+2\sqrt{3}}}}$$C=\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{\left(\sqrt{3}+1\right)^2}}}$$C=\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{3}-1}}$$C=\sqrt{6+2\sqrt{2}.\sqrt{2-\sqrt{3}}}$$C=\sqrt{6+2\sqrt{4-2\sqrt{3}}}$$C=\sqrt{6+2\sqrt{\left(\sqrt{3}-1\right)^2}}$$C=\sqrt{6+2.\left(\sqrt{3}-1\right)}$$C=\sqrt{6+2\sqrt{3}-2}$$C=\sqrt{4+2\sqrt{3}}$$C=\sqrt{\left(\sqrt{3}+1\right)^2}=\sqrt{3}+1$

Tạ Đức Hoàng Anh · Answer

1) Ta có: $\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}}$         $=\sqrt{2+2\sqrt{2}+1}+\sqrt{2-2\sqrt{2}+1}$         $=\sqrt{\left(\sqrt{2}+1\right)^2}+\sqrt{\left(\sqrt{2}-1\right)^2}$         $=\sqrt{2}+1+\sqrt{2}-1$         $=2\sqrt{2}\approx2,82843$2) Ta có: $B=\frac{\sqrt{15}-\sqrt{6}}{\sqrt{35}-\sqrt{14}}$        $\Leftrightarrow B=\frac{\sqrt{5}.\sqrt{3}-\sqrt{2}.\sqrt{3}}{\sqrt{5}.\sqrt{7}-\sqrt{2}.\sqrt{7}}$        $\Leftrightarrow B=\frac{\sqrt{3}.\left(\sqrt{5}-\sqrt{2}\right)}{\sqrt{7}.\left(\sqrt{5}-\sqrt{2}\right)}$        $\Leftrightarrow B=\frac{\sqrt{3}}{\sqrt{7}}\approx0,65465$3) Ta có: $C=\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{4+2\sqrt{3}}}}$        $\Leftrightarrow C=\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{3+2\sqrt{3}+1}}}$        $\Leftrightarrow C=\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{\left(\sqrt{3}+1\right)^2}}}$        $\Leftrightarrow C=\sqrt{6+\sqrt{8}.\sqrt{3-\sqrt{3}-1}}$        $\Leftrightarrow C=\sqrt{6+\sqrt{2.8-2.2.\sqrt{3}.2}}$        $\Leftrightarrow C=\sqrt{6+\sqrt{12-2.\sqrt{4.3}.2+1}}$        $\Leftrightarrow C=\sqrt{6+\sqrt{12-2.\sqrt{12}.2+4}}$        $\Leftrightarrow C=\sqrt{6+\sqrt{\left(\sqrt{12}-2\right)^2}}$        $\Leftrightarrow C=\sqrt{6+\sqrt{12}-2}$        $\Leftrightarrow C=\sqrt{3+2\sqrt{3}+1}$        $\Leftrightarrow C=\sqrt{\left(\sqrt{3}+1\right)^2}$        $\Leftrightarrow C=\sqrt{3}+1\approx2,73205$Câu trả lời: 1) Ta có: $\sqrt{3+2\sqrt{2}}+\sqrt{3-2\sqrt{2}}$         $=\sqrt{2+2\sqrt{2}+1}+\sqrt{2-2\sqrt{2}+1}$         $=\sqrt{\left(\sqrt{2}+1\right)^2}+\sqrt{\left(\sqrt{2}-1\right)^2}$         $=\sqrt{2}+1+\sqrt{2}-1$         $=2\sqrt{2}\approx2,82843$2) Ta có: $B=\frac{\sqrt{15}-\sqrt{6}}{\sqrt{35}-\sqrt{14}}$        $\Leftrightarrow B=\frac{\sqrt{5}.\sqrt{3}-\sqrt{2}.\sqrt{3}}{\sqrt{5}.\sqrt{7}-\sqrt{2}.\sqrt{7}}$        $\Leftrightarrow B=\frac{\sqrt{3}.\left(\sqrt{5}-\sqrt{2}\right)}{\sqrt{7}.\left(\sqrt{5}-\sqrt{2}\right)}$        $\Leftrightarrow B=\frac{\sqrt{3}}{\sqrt{7}}\approx0,65465$3) Ta có: $C=\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{4+2\sqrt{3}}}}$        $\Leftrightarrow C=\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{3+2\sqrt{3}+1}}}$        $\Leftrightarrow C=\sqrt{6+2\sqrt{2}.\sqrt{3-\sqrt{\left(\sqrt{3}+1\right)^2}}}$        $\Leftrightarrow C=\sqrt{6+\sqrt{8}.\sqrt{3-\sqrt{3}-1}}$        $\Leftrightarrow C=\sqrt{6+\sqrt{2.8-2.2.\sqrt{3}.2}}$        $\Leftrightarrow C=\sqrt{6+\sqrt{12-2.\sqrt{4.3}.2+1}}$        $\Leftrightarrow C=\sqrt{6+\sqrt{12-2.\sqrt{12}.2+4}}$        $\Leftrightarrow C=\sqrt{6+\sqrt{\left(\sqrt{12}-2\right)^2}}$        $\Leftrightarrow C=\sqrt{6+\sqrt{12}-2}$        $\Leftrightarrow C=\sqrt{3+2\sqrt{3}+1}$        $\Leftrightarrow C=\sqrt{\left(\sqrt{3}+1\right)^2}$        $\Leftrightarrow C=\sqrt{3}+1\approx2,73205$

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