Câu hỏi của Chuột yêu Gạo

Question

Rút gọn biểu thức:

$a,\sqrt{\sqrt{17+12\sqrt{2}}}$

$b,\sqrt{4+2\sqrt{3}}-\sqrt{21-12\sqrt{3}}$

Trần Thanh Phương · Accepted Answer

a) $\sqrt{\sqrt{17+12\sqrt{2}}}$

$=\sqrt{\sqrt{\left(2\sqrt{2}\right)^2+2\cdot2\sqrt{2}\cdot3+9}}$

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

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

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

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

$=\sqrt{2}+1$Câu trả lời: a) $\sqrt{\sqrt{17+12\sqrt{2}}}$

$=\sqrt{\sqrt{\left(2\sqrt{2}\right)^2+2\cdot2\sqrt{2}\cdot3+9}}$

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

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

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

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

$=\sqrt{2}+1$

Trần Thanh Phương · Answer

b) $\sqrt{4+2\sqrt{3}}-\sqrt{21-12\sqrt{3}}$

$=\sqrt{3+2\sqrt{3}+1}-\sqrt{\left(2\sqrt{2}\right)^2-2\cdot2\sqrt{2}\cdot3+9}$

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

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

$=\sqrt{3}+2\sqrt{2}-2$Câu trả lời: b) $\sqrt{4+2\sqrt{3}}-\sqrt{21-12\sqrt{3}}$

$=\sqrt{3+2\sqrt{3}+1}-\sqrt{\left(2\sqrt{2}\right)^2-2\cdot2\sqrt{2}\cdot3+9}$

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

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

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

Violympic toán 9