Câu hỏi của Nguyễn Anh Khoa

Question

Tính giá trị biểu thức:

$A=\sqrt{6+\sqrt{24}+\sqrt{12}+\sqrt{8}}-\sqrt{4+2\sqrt{3}}$

Trần Việt Linh · Accepted Answer

$A=\sqrt{6+\sqrt{24}+\sqrt{12}+\sqrt{8}}-\sqrt{4+2\sqrt{3}}$

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

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

$=1+\sqrt{2}+\sqrt{3}+\sqrt{3}+1=\sqrt{2}+2\sqrt{3}+2$

Câu trả lời:

$A=\sqrt{6+\sqrt{24}+\sqrt{12}+\sqrt{8}}-\sqrt{4+2\sqrt{3}}$

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

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

$=1+\sqrt{2}+\sqrt{3}+\sqrt{3}+1=\sqrt{2}+2\sqrt{3}+2$