Question

Rút gọn căn bậc hai theo hằng đẳng thức:

\(\sqrt{11+4\sqrt{6}}\)

Answer 1

\(\sqrt{11+4\sqrt{6}}=\sqrt{8+4\sqrt{6}+3}=\sqrt{\left(2\sqrt{2}+\sqrt{3}\right)^2}=2\sqrt{2}+\sqrt{3}\)

Answer 2

\(\sqrt{11+4\sqrt{6}}\)=\(\sqrt{\left(2\sqrt{2}\right)^2+2.2\sqrt{2}.\sqrt{3}+\left(\sqrt{3}\right)^3}\)=\(\sqrt{\left(2\sqrt{2}+\sqrt{3}\right)^2}\)=\(2\sqrt{2}\)+\(\sqrt{3}\)