Question

thực hiện phép tính \(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)

Answer 1

Bài làm:

\(\sqrt{14-8\sqrt{3}}-\sqrt{24-12\sqrt{3}}\)

\(=\sqrt{8-8\sqrt{3}+6}-\sqrt{18-12\sqrt{3}+6}\)

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

\(=2\sqrt{2}-\sqrt{6}-3\sqrt{2}+\sqrt{6}\)

\(=-\sqrt{2}\)

Học tốt 

Answer 2

\(\sqrt{3.2-8\sqrt{3}+4.2}=\sqrt{\left(\sqrt{3}.\sqrt{2}\right)^2-2.2.\sqrt{2}.\sqrt{2}.\sqrt{3}+\left(2\sqrt{2}\right)^2}\)

\(=\sqrt{\left(2\sqrt{2}-\sqrt{6}\right)^2}-\sqrt{3^2.2-12\sqrt{3}+3.2}=2\sqrt{2}-\sqrt{6}-3\sqrt{2}+\sqrt{6}=-\sqrt{2}\)