Câu hỏi của Nguyễn Phúc Thiên

Question

Tính

$\sqrt{6+\sqrt{8}+\sqrt{12}+\sqrt{24}}$

$\frac{\sqrt{3}}{\sqrt{\sqrt{6}+1}-1}-\frac{\sqrt{3}}{\sqrt{\sqrt{6}+1}+1}$

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Đàm Thị Minh Hương · Accepted Answer

$\sqrt{6+\sqrt{8}+\sqrt{12}+\sqrt{24}}=\sqrt{6+2\sqrt{2}+2\sqrt{3}+2\sqrt{6}}$

$=\sqrt{2+3+1+2\sqrt{2}+2\sqrt{3}+2\sqrt{6}}$$=\sqrt{\left(\sqrt{2}+\sqrt{3}+1\right)^2}=\left|\sqrt{2}+\sqrt{3}+1\right|=\sqrt{2}+\sqrt{3}+1$

Câu trả lời:

$\sqrt{6+\sqrt{8}+\sqrt{12}+\sqrt{24}}=\sqrt{6+2\sqrt{2}+2\sqrt{3}+2\sqrt{6}}$

$=\sqrt{2+3+1+2\sqrt{2}+2\sqrt{3}+2\sqrt{6}}$$=\sqrt{\left(\sqrt{2}+\sqrt{3}+1\right)^2}=\left|\sqrt{2}+\sqrt{3}+1\right|=\sqrt{2}+\sqrt{3}+1$