Question

Rút gọn biểu thức :

\(\sqrt{37-20\sqrt{3}}-\sqrt{37+20\sqrt{3}}\)

Answer 1

= \(\sqrt{12-2.2\sqrt{3}.5+25}-\sqrt{12+2.2\sqrt{3}.5+25}\)

= \(\sqrt{\left(2\sqrt{3}-5\right)^2}-\sqrt{\left(2\sqrt{3}+5\right)^2}\)

= \(|2\sqrt{3}-5|-2\sqrt{3}-5\)

=\(5-2\sqrt{3}-2\sqrt{3}-5=-4\sqrt{3}\)

Answer 2

bây giờ vẫn còn công chúa

Answer 3

Trả lời:

\(\sqrt{37-20\sqrt{3}}-\sqrt{37+20\sqrt{3}}\)

\(=\sqrt{25-20\sqrt{3}+12}-\sqrt{25+20\sqrt{3}+12}\)

\(=\sqrt{\left(5-2\sqrt{3}\right)^2}-\sqrt{\left(5+2\sqrt{3}\right)^2}\)

\(=5-2\sqrt{3}-5-2\sqrt{3}\)

\(=-4\sqrt{3}\)