Câu hỏi của Nguyễn Thu Huyền

Question

Rút gọn biểu thức: $N=\sqrt{4\sqrt{6}+8\sqrt{3}+4\sqrt{2}+18}$

Trần Thanh Phương · Accepted Answer

$N=\sqrt{4\sqrt{6}+8\sqrt{3}+4\sqrt{2}+18}$

$N=\sqrt{12+4+2+2\cdot2\sqrt{3}\cdot\sqrt{2}+2\cdot2\sqrt{3}\cdot2+2\cdot2\cdot\sqrt{2}}$

$N=\sqrt{\left(2\sqrt{3}\right)^2+2^2+\left(\sqrt{2}\right)^2+2\cdot2\sqrt{3}\cdot\sqrt{2}+2\cdot2\sqrt{3}\cdot2+2\cdot2\cdot\sqrt{2}}$

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

$N=2+2\sqrt{3}+\sqrt{2}$Câu trả lời: $N=\sqrt{4\sqrt{6}+8\sqrt{3}+4\sqrt{2}+18}$

$N=\sqrt{12+4+2+2\cdot2\sqrt{3}\cdot\sqrt{2}+2\cdot2\sqrt{3}\cdot2+2\cdot2\cdot\sqrt{2}}$

$N=\sqrt{\left(2\sqrt{3}\right)^2+2^2+\left(\sqrt{2}\right)^2+2\cdot2\sqrt{3}\cdot\sqrt{2}+2\cdot2\sqrt{3}\cdot2+2\cdot2\cdot\sqrt{2}}$

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

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

Violympic toán 9