Question

\(\sqrt{11+2\left(\sqrt{6}+\sqrt{12}+\sqrt{18}\right)}\) . Làm sao để đưa về bình phương. Giair ra giúp mình nhé 

Answer 1

Nhìn nó có dạng \(\sqrt{\left(\sqrt{a}+\sqrt{b}+\sqrt{c}\right)^2}=\sqrt{a+b+c+2\left(\sqrt{ab}+\sqrt{bc}+\sqrt{ca}\right)}\)

Thấy \(2\left(\sqrt{6}+\sqrt{12}+\sqrt{18}\right)=2\left(\sqrt{2.3}+\sqrt{2.6}+\sqrt{3.6}\right)\)

nên:

\(\sqrt{11+2\left(\sqrt{6}+\sqrt{12}+\sqrt{18}\right)}=\sqrt{\sqrt{2}^2+\sqrt{6}^2+\sqrt{3}^2+2\left(\sqrt{2.3}+\sqrt{2.6}+\sqrt{3.6}\right)}\)

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