Question

Rút gọn biểu thức:

\(a,\sqrt{33+20\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)

\(b,\sqrt{94-42\sqrt{5}}-\sqrt{94+42\sqrt{5}}\)

Answer 1

\(a,\sqrt{33+20\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)

\(=\sqrt{8+2.2\sqrt{2}.5+25}-\sqrt{2-2.\sqrt{2}.3+9}\)

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

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

\(=2+\sqrt{2}\)

chúc bn học tốt

Answer 2

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

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

b)\(\sqrt{\left(7-3\sqrt{5}\right)^2}-\sqrt{\left(7+3\sqrt{5}\right)^2}=7-3\sqrt{5}-7-3\sqrt{5}=-6\sqrt{5}\)